Finite Group Databasebeta

C2×#19134639 #25096237

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#19134639

Splittings

SylowC43 ⋊ C2×#1812

Subgroups

subgroupG/H
centerC2×C4#13063281
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#410C2
socleC22×C43#380
prime radicalC22×#41×C43C22
cosocleC22×C4×C43C24
hypercenterC2×#410D43
hypocenterC43C2×#1812
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#410

1346 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 169208);