Finite Group Databasebeta

C2×#19132556 #25006328

order11008
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#19132556

Splittings

SylowC43 ⋊ C2×#1331

Subgroups

subgroupG/H
centerC22×C4#10621882
commutatorC8×C43C22×C8
FrattiniC4×C8C22×D43
FittingC2×C4×D8×C43C2
socleC23×C43#102
prime radicalC22×D8×C43C4
cosocleC4×C8×C43C23
hypercenterC2×C4×D8D43
hypocenterC43C2×#1331
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×D8

470 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1264 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 79299);