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C4×#15668057 #26033457

order11392
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×#15668057

Splittings

FittingC2×C4×D4×C89 ⋊ C2
SylowC89 ⋊ C4×H(5,𝔽2)

Subgroups

subgroupG/H
centerC2×C4C23×D89
commutatorC2×C89C24×C4
FrattiniC22C24×D89
FittingC2×C4×D4×C89C2
socle, cosocleC22×C89C25
prime radicalC2×#15668057C2
hypercenterC2×C4×D4D89
hypocenterC89C4×H(5,𝔽2)
LCSG ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ C2×C4×D4

1660 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1828 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#36445819, #36445820, #36445826, …
maximal normal subgroup of#36445819, #36445820, #36445826, …
maximal quotient ofC4×#19152071, C4×#19152070, C4×#19152073, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 17715);