Finite Group Databasebeta

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C4⋊C4×Dic71⋊C4 #31918889

order18176
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4⋊C4×Dic71⋊C4

Splittings

SylowC71 ⋊ C4⋊C42

Subgroups

subgroupG/H
center, FrattiniC24C23×D71
commutatorC22×C71C22×C42
FittingC2×C4×C4⋊C4×C71C2
socle, prime radical, cosocleC24×C71C24
hypercenterC2×C4×C4⋊C4D71
hypocenterC71C4⋊C42
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

1838 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18176

Conjugacy classes & character table

2900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 91005);