Finite Group Databasebeta

← Prev (#26022777) Next (#26022779) →

C4×#15667997 #26022778

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

Aliases

direct productC4×#15667997

Splittings

FittingC4×C4⋊C4×C89 ⋊ C2
SylowC89 ⋊ C4×#123

Subgroups

subgroupG/H
centerC22×C4C22×D89
commutatorC22×C89C23×C4
FrattiniC23C23×D89
FittingC4×C4⋊C4×C89C2
socle, cosocleC23×C89C24
prime radicalC22×D356C22
hypercenterC4×C4⋊C4D89
hypocenterC89C4×#123
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

688 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#36561386, C8×#15667997, #36561397, …
maximal normal subgroup of#36561386, C8×#15667997, #36561397, …
maximal quotient ofC4×#19151476, C4×#19151487, C4×#19151488, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 7036);