Finite Group Databasebeta

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D4×C4⋊C4×D71 #32156732

order18176
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productD4×C4⋊C4×D71

Splittings

FittingD4×C4⋊C4×C71 ⋊ C2
SylowC71 ⋊ C2×D4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C24×D71
commutatorC22×C71C24×C4
FittingD4×C4⋊C4×C71C2
socle, cosocleC23×C71C25
prime radicalC22×D4×D71C22
hypercenterD4×C4⋊C4D71
hypocenterC71C2×D4×C4⋊C4
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ D4×C4⋊C4

4718 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4544

Conjugacy classes & character table

1850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 328848);