Finite Group Databasebeta

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C4×C4⋊Q8×D71 #32155968

order18176
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×C4⋊Q8×D71

Splittings

FittingC4×C4⋊Q8×C71 ⋊ C2
SylowC71 ⋊ C2×C4×C4⋊Q8

Subgroups

subgroupG/H
centerC22×C4C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC4×C4⋊Q8×C71C2
socle, cosocleC23×C71C25
prime radicalC23×D71C24
hypercenterC4×C4⋊Q8D71
hypocenterC71C2×C4×C4⋊Q8
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C4×C4⋊Q8

3358 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

2072 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 328084);