Finite Group Databasebeta

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C22×C4×C8×D71 #32860830

order18176
automorphism?
homologyAbelianization (H1) = C23×C4×C8 · Schur multiplier (H2) = C29×C4

Aliases

direct productC22×C4×C8×D71

Splittings

FittingC22×C4×C8×C71 ⋊ C2
derived, SylowC71 ⋊ C23×C4×C8

Subgroups

subgroupG/H
center, hypercenterC22×C4×C8D71
commutator, hypocenterC71C23×C4×C8
FrattiniC2×C4C24×D71
FittingC22×C4×C8×C71C2
socleC24×C71C22×C4
prime radicalC24×D71C2×C4
cosocleC2×C4×C71C25
LCSG ▷ C71
UCSC1 ◁ C22×C4×C8

4638 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

4736 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 1032946);