Finite Group Databasebeta

C2×#19133481 #25066326

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

Aliases

direct productC2×#19133481

Splittings

FittingC2×C82×C43 ⋊ C2
SylowC43 ⋊ C2×#1589

Subgroups

subgroupG/H
centerC22×C4C2×D172
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC2×C82×C43C2
socleC23×C43C4×D4
prime radicalC22×D344C4
cosocleC42×C43C24
hypercenterC2×C82D43
hypocenterC43C2×#1589
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×C82

822 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2776 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 139297);