Finite Group Databasebeta

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C4×#15668008 #26022815

order11392
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×#15668008

Splittings

FittingC2×C4×D4×C89 ⋊ C2
SylowC89 ⋊ C4×#127

Subgroups

subgroupG/H
centerC22×C4C22×D89
commutatorC22×C89C23×C4
FrattiniC23C23×D89
FittingC2×C4×D4×C89C2
socle, cosocleC23×C89C24
prime radicalC2×#15668008C2
hypercenterC2×C4×D4D89
hypocenterC89C4×#127
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

924 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1816 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#36449080, #36449081, #36449083, …
maximal normal subgroup of#36449080, #36449081, #36449083, …
maximal quotient ofC4×#19151498, C4×#19151501, C4×#19151499, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 7073);