Finite Group Databasebeta

C2×#19132734 #25016797

order11008
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productC2×#19132734

Splittings

FittingC2×C43×M64 ⋊ C2
SylowC43 ⋊ C2×#1400

Subgroups

subgroupG/H
centerC2×C8(C2×D43)⋊C4
commutatorC22×C43C22×C16
FrattiniC2×C16C22×D43
FittingC2×C43×M64C2
socleC22×C43C22⋊C16
prime radicalC23×D43C16
cosocleC2×C16×C43C23
hypercenterC2×M64D43
hypocenterC43C2×#1400
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C8 ◁ C22×C16 ◁ C2×M64

306 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, 89768);