Finite Group Databasebeta

← Prev (#26022786) Next (#26022788) →

C4×#15667991 #26022787

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

Aliases

direct productC4×#15667991

Splittings

SylowC89 ⋊ C4×C22⋊Q8

Subgroups

subgroupG/H
centerC22×C4C22×D89
commutatorC22×C89C23×C4
FrattiniC23C23×D89
FittingC22×C42×C89C2
socle, cosocleC23×C89C24
prime radicalC24×C89C23
hypercenterC22×C42D89
hypocenterC89C4×C22⋊Q8
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C22×C4 ◁ C22×C42

656 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2872 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#36442390, #36442393, #36442463, …
maximal normal subgroup of#36442390, #36442393, #36442463, …
maximal quotient ofC4×#19151471, C4×#19151482, C4×#19151496, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 7045);