Finite Group Databasebeta

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C4×#15667989 #26022783

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

Aliases

direct productC4×#15667989

Splittings

SylowC89 ⋊ C4×C22⋊Q8

Subgroups

subgroupG/H
centerC22×C4C22×D89
commutatorC22×C89C23×C4
FrattiniC23C23×D89
FittingC4×C22⋊C4×C89C2
socle, cosocleC23×C89C24
prime radicalC24×C89C23
hypercenterC4×C22⋊C4D89
hypocenterC89C4×C22⋊Q8
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

656 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 ofC8×#15667989, #36561839, #36561849, …
maximal normal subgroup ofC8×#15667989, #36561839, #36561849, …
maximal quotient ofC4×#19151473, C4×#19151470, C4×#19151485, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 7041);