Finite Group Databasebeta

C8×#14556159 #31966877

order18176
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC8×#14556159

Splittings

FittingC2×C8×Q8×C71 ⋊ C2
SylowC71 ⋊ C8×#137

Subgroups

subgroupG/H
centerC2×C8C2×C22⋊D71
commutatorC4×C71C23×C8
FrattiniC42C23×D71
FittingC2×C8×Q8×C71C2
socleC22×C71C2×C4×D4
prime radicalC2×#11765865C2×C4
cosocleC42×C71C24
hypercenterC2×C8×Q8D71
hypocenterC71C8×#137
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C8 ◁ C2×C4×C8 ◁ C2×C8×Q8

714 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

2888 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 138993);