Finite Group Databasebeta

C8×#14556122 #32005665

order18176
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24

Aliases

direct productC8×#14556122

Splittings

FittingC42×C8×C71 ⋊ C2
SylowC71 ⋊ C8×#126

Subgroups

subgroupG/H
centerC22×C8C22×D71
commutatorC22×C71C23×C8
FrattiniC22×C4C23×D71
FittingC42×C8×C71C2
socleC23×C71C23×C4
prime radicalC23×D71C22×C4
cosocleC22×C4×C71C24
hypercenterC42×C8D71
hypocenterC71C8×#126
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C8 ◁ C42×C8

786 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

4592 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 177781);