Finite Group Databasebeta

C2×#19152397 #26034998

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

Aliases

direct productC2×#19152397

Splittings

FittingC2×#137×C89 ⋊ C2
SylowC89 ⋊ C2×#575

Subgroups

subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC4×C89C25
FrattiniC4C24×D89
FittingC2×#137×C89C2
socleC22×C89C22×D4
hypercenterC2×#137D89
hypocenterC89C2×#575
LCSG ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

1484 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#36555930, #36555939, #36556297, …
maximal normal subgroup of#36555930, #36555939, #36556297, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 19256);