Extensions 1→N→G→Q→1 with N=C₃ and Q=C₆²⋊₅C₄

Direct product G=N×Q with N=C₃ and Q=C₆²⋊₅C₄

		d	ρ	Label	ID
C₃×C₆²⋊₅C₄		72		C3xC6^2:5C4	432,495

Semidirect products G=N:Q with N=C₃ and Q=C₆²⋊₅C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₆²⋊₅C₄) = C₆².₇₇D₆	φ: C₆²⋊₅C₄/C₂×C₃⋊Dic₃ → C₂ ⊆ Aut C₃	144		C3:1(C6^2:5C4)	432,449
C₃⋊₂(C₆²⋊₅C₄) = C₆³.C₂	φ: C₆²⋊₅C₄/C₂×C₆² → C₂ ⊆ Aut C₃	216		C3:2(C6^2:5C4)	432,511

Non-split extensions G=N.Q with N=C₃ and Q=C₆²⋊₅C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₆²⋊₅C₄) = C₆².₁₂₇D₆	φ: C₆²⋊₅C₄/C₂×C₆² → C₂ ⊆ Aut C₃	216		C3.(C6^2:5C4)	432,198
C₃.₂(C₆²⋊₅C₄) = C₆²⋊₄Dic₃	central stem extension (φ=1)	72		C3.2(C6^2:5C4)	432,199

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Extensions 1→N→G→Q→1 with N=C3 and Q=C62⋊5C4