Finite Group Databasebeta

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C4×#17985921 #31919308

order18176
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×#17985921

Splittings

FittingC2×C4×C4⋊C4×C71 ⋊ C2
SylowC71 ⋊ C4×#396

Subgroups

subgroupG/H
centerC23×C4C22×D71
commutatorC23×C71C23×C4
FrattiniC24C23×D71
FittingC2×C4×C4⋊C4×C71C2
socle, cosocleC24×C71C24
prime radicalC24×D71C23
hypercenterC2×C4×C4⋊C4D71
hypocenterC71C4×#396
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

1966 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, 91424);