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H(3,ℤ/4)×Dic89 #36459591

order22784
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C2×C43

Aliases

direct productH(3,ℤ/4)×Dic89

Splittings

SylowC89 ⋊ C4×H(3,ℤ/4)

Subgroups

subgroupG/H
centerC2×C4C42×D89
commutatorC4×C89C43
FrattiniC23×C4C22×D89
FittingC2×H(3,ℤ/4)×C89C2
socleC22×C89C2×#95
prime radicalC24×C89C2×D4
cosocleC23×C4×C89C23
hypercenterC2×H(3,ℤ/4)D89
hypocenterC89C4×H(3,ℤ/4)
LCSG ▷ C4×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ C2×H(3,ℤ/4)

954 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5696

Conjugacy classes & character table

2024 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 74731);