Finite Group Databasebeta

C2×#19132642 #25007834

order11008
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#19132642

Splittings

FittingC2×C43×C4⋊C16 ⋊ C2
SylowC43 ⋊ C2×#1361

Subgroups

subgroupG/H
centerC23#13063247
commutatorC2×C8×C43C22×C4
FrattiniC4×C8C22×D43
FittingC2×C43×C4⋊C16C2
socleC23×C43#102
prime radicalC2×#14583276C2
cosocleC4×C8×C43C23
hypercenterC2×C4⋊C16D43
hypocenterC43C2×#1361
LCSG ▷ C2×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4⋊C16

518 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1738 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 80805);