Finite Group Databasebeta

C2×#19135602 #25123392

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#19135602

Splittings

FittingC23×Q16×C43 ⋊ C2
SylowC43 ⋊ C2×#2001

Subgroups

subgroupG/H
centerC24D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC23×Q16×C43C2
socleC24×C43C2×D4
prime radicalC24×D43D4
hypercenterC23×Q16D43
hypocenterC43C2×#2001
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×Q16

2182 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 196363);