Finite Group Databasebeta

C2×#19134519 #25095750

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#19134519

Splittings

SylowC43 ⋊ C2×#1784

Subgroups

subgroupG/H
centerC23C2×C22⋊Dic43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC24×Q8×C43C2
socleC23×C43C2×C22⋊C4
prime radicalC25×C43C2×C4
cosocleC22×C4×C43C24
hypercenterC24×Q8D43
hypocenterC43C2×#1784
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ C24×Q8

3798 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1744 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 168721);