Finite Group Databasebeta

C2×#19134506 #25095703

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

Aliases

direct productC2×#19134506

Splittings

FittingC22×C22⋊C8×C43 ⋊ C2
SylowC43 ⋊ C2×#1780

Subgroups

subgroupG/H
centerC23×C4C22×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×C22⋊C8×C43C2
socleC24×C43C22×C4
prime radicalC23×#10621898C2
cosocleC22×C4×C43C24
hypercenterC22×C22⋊C8D43
hypocenterC43C2×#1780
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C22×C22⋊C8

4070 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 168674);