Finite Group Databasebeta

C2×#19152410 #26035013

order11392
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#19152410

Splittings

FittingC2×#131×C89 ⋊ C2
SylowC89 ⋊ C2×#577

Subgroups

subgroupG/H
centerC22C22×D356
commutator, cosocleC4×C89C25
FrattiniC4C24×D89
FittingC2×#131×C89C2
socleC22×C89C22×D4
hypercenterC2×#131D89
hypocenterC89C2×#577
LCSG ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131

1460 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1804 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#36570339, #36570345, #36570366, …
maximal normal subgroup of#36570339, #36570345, #36570366, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 19271);