Finite Group Databasebeta

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C4×#15667987 #26022767

order11392
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×#15667987

Splittings

FittingC4×C4⋊C4×C89 ⋊ C2
SylowC89 ⋊ C4×#121

Subgroups

subgroupG/H
centerC22×C4C22×D89
commutatorC22×C89C23×C4
FrattiniC23C23×D89
FittingC4×C4⋊C4×C89C2
socle, cosocleC23×C89C24
prime radicalC2×#15667987C2
hypercenterC4×C4⋊C4D89
hypocenterC89C4×#121
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

824 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#36448958, #36448963, #36448978, …
maximal normal subgroup of#36448958, #36448963, #36448978, …
maximal quotient ofC4×#19151476, C4×#19151490, C4×#19151499, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 7025);