Finite Group Databasebeta

C8×#14556086 #31995654

order18176
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C23×C42

Aliases

direct productC8×#14556086

Splittings

FittingC8×C4⋊C4×C71 ⋊ C2
SylowC71 ⋊ C8×#117

Subgroups

subgroupG/H
centerC22×C8C22×D71
commutatorC2×C71C22×C4×C8
FrattiniC22×C4C23×D71
FittingC8×C4⋊C4×C71C2
socleC23×C71C23×C4
prime radicalC23×D71C22×C4
cosocleC22×C4×C71C24
hypercenterC8×C4⋊C4D71
hypocenterC71C8×#117
LCSG ▷ C2×C71 ▷ C71
UCSC1 ◁ C22×C8 ◁ C8×C4⋊C4

1174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

2960 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 167770);