Finite Group Databasebeta

C2×#19132531 #25005716

order11008
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#19132531

Splittings

SylowC43 ⋊ C2×#1320

Subgroups

subgroupG/H
centerC2×C4#13063240
commutatorC23×C43C22×C8
FrattiniC2×M16C22×D43
FittingC2×C43×#407C2
socleC22×C43#323
prime radicalC25×C43C8
cosocleC2×M16×C43C23
hypercenterC2×#407D43
hypocenterC43C2×#1320
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×M16 ◁ C2×#407

626 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1228 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 78687);