Finite Group Databasebeta

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C2×C4×C4⋊C4×D71 #32155628

order18176
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4

Aliases

direct productC2×C4×C4⋊C4×D71

Splittings

FittingC2×C4×C4⋊C4×C71 ⋊ C2
SylowC71 ⋊ C22×C4×C4⋊C4

Subgroups

subgroupG/H
centerC23×C4C22×D71
commutatorC2×C71C23×C42
FrattiniC23C24×D71
FittingC2×C4×C4⋊C4×C71C2
socleC24×C71C24
prime radicalC24×D71C23
cosocleC23×C71C25
hypercenterC2×C4×C4⋊C4D71
hypocenterC71C22×C4×C4⋊C4
LCSG ▷ C2×C71 ▷ C71
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

5758 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, 327744);