Finite Group Databasebeta

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C4×C4⋊C8×D71 #31995321

order18176
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×C4⋊C8×D71

Splittings

FittingC4×C4⋊C8×C71 ⋊ C2
SylowC71 ⋊ C2×C4×C4⋊C8

Subgroups

subgroupG/H
centerC2×C42C22×D71
commutatorC2×C71C22×C4×C8
FrattiniC22×C4C23×D71
FittingC4×C4⋊C8×C71C2
socleC23×C71C23×C4
prime radicalC23×D71C22×C4
cosocleC22×C4×C71C24
hypercenterC4×C4⋊C8D71
hypocenterC71C2×C4×C4⋊C8
LCSG ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C42 ◁ C4×C4⋊C8

1550 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

2960 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 167437);