Finite Group Databasebeta

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C4⋊C4×#13083564 #36572857

order22784
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4⋊C4×#13083564

Splittings

SylowC89 ⋊ C4⋊C4×Q16

Subgroups

subgroupG/H
centerC23C22×C22⋊D89
commutatorC2×C4×C89C23×C4
FrattiniC22×C4C23×D89
FittingQ8×C4⋊C4×C89C2
socle, prime radicalC23×C89C22×D4
cosocleC22×C4×C89C24
hypercenterQ8×C4⋊C4D89
hypocenterC89C4⋊C4×Q16
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ Q8×C4⋊C4

926 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22784

Conjugacy classes & character table

2270 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 187997);