Finite Group Databasebeta

C2×#19152396 #26034997

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

Aliases

direct productC2×#19152396

Splittings

FittingC22×#41×C89 ⋊ C2
SylowC89 ⋊ C2×#575

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊D89
commutator, cosocleC4×C89C25
FrattiniC4C24×D89
FittingC22×#41×C89C2
socleC22×C89C22×D4
hypercenterC22×#41D89
hypocenterC89C2×#575
LCSG ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#41

1484 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#36461196, #36461197, #36461200, …
maximal normal subgroup of#36461196, #36461197, #36461200, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 19255);