Finite Group Databasebeta

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C4×#17986391 #32006001

order18176
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#17986391

Splittings

FittingC4×C4⋊Q8×C71 ⋊ C2
SylowC71 ⋊ C4×#497

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC4×C4⋊Q8×C71C2
socleC23×C71C22×D4
prime radicalC22×D284C23
cosocleC22×C4×C71C24
hypercenterC4×C4⋊Q8D71
hypocenterC71C4×#497
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×C4⋊Q8

1094 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

2024 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 178117);