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C
n
D
n
S
n
A
n
Degree
Linear
Irr Reps
Characters
×
⋊
.
○
≀
Extensions
1→N→G→Q→1 with N=
C
7
and Q=
C
2
×C
32
Direct product G=N×Q with N=
C
7
and Q=
C
2
×C
32
d
ρ
Label
ID
C
2
×C
224
448
C2xC224
448,173
Semidirect products G=N:Q with N=
C
7
and Q=
C
2
×C
32
extension
φ:Q→Aut N
d
ρ
Label
ID
C
7
⋊
1
(C
2
×C
32
) =
D
7
×C
32
φ:
C
2
×C
32
/
C
32
→
C
2
⊆ Aut
C
7
224
2
C7:1(C2xC32)
448,3
C
7
⋊
2
(C
2
×C
32
) =
C
2
×C
7
⋊C
32
φ:
C
2
×C
32
/
C
2
×C
16
→
C
2
⊆ Aut
C
7
448
C7:2(C2xC32)
448,55
×
⋊
ℤ
𝔽
○
≀
ℚ
◁