Finite Group Databasebeta

C2×#19151521 #26023473

order11392
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#19151521

Splittings

SylowC89 ⋊ C2×#396

Subgroups

subgroupG/H
centerC24C22×D89
commutator, cosocleC23×C89C24
FrattiniC23C23×D89
FittingC22×C22⋊C4×C89C2
socleC24×C89C23
prime radicalC25×C89C22
hypercenterC22×C22⋊C4D89
hypocenterC89C2×#396
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C24 ◁ C22×C22⋊C4

908 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#36476283, C4×#19151521, #36480068, …
maximal normal subgroup of#36476283, C4×#19151521, #36480068, …
maximal quotient ofC2×#26018495, C2×#26018497, C2×#26018503, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 7731);