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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
4
.
10
D
4
Direct product G=N×Q with N=
C
7
and Q=
C
4
.
10
D
4
d
ρ
Label
ID
C
7
×C
4
.
10
D
4
112
4
C7xC4.10D4
224,50
Semidirect products G=N:Q with N=
C
7
and Q=
C
4
.
10
D
4
extension
φ:Q→Aut N
d
ρ
Label
ID
C
7
⋊
1
(C
4
.
10
D
4
) =
C
4
.
12
D
28
φ:
C
4
.
10
D
4
/
M
4
(2)
→
C
2
⊆ Aut
C
7
112
4-
C7:1(C4.10D4)
224,30
C
7
⋊
2
(C
4
.
10
D
4
) =
C
28
.
10
D
4
φ:
C
4
.
10
D
4
/
C
2
×Q
8
→
C
2
⊆ Aut
C
7
112
4
C7:2(C4.10D4)
224,42
×
⋊
ℤ
𝔽
○
≀
ℚ
◁