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C4⋊C4×#13083549 #36469772

order22784
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4⋊C4×#13083549

Splittings

SylowC89 ⋊ C16×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22×C8C22×D89
commutatorC2×C89C2×C4×C16
FittingC8×C4⋊C4×C89C2
socle, prime radicalC23×C89C22×C8
cosocleC22×C8×C89C23
hypercenterC8×C4⋊C4D89
hypocenterC89C16×C4⋊C4
LCSG ▷ C2×C89 ▷ C89
UCSC1 ◁ C22×C8 ◁ C8×C4⋊C4

398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22784

Conjugacy classes & character table

3680 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 84912);