Finite Group Databasebeta

C2×#19135277 #25099201

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

Aliases

direct productC2×#19135277

Splittings

FittingC2×C43×#389 ⋊ C2
SylowC43 ⋊ C2×#1934

Subgroups

subgroupG/H
centerC24C2×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#389C2
socleC24×C43C2×D4
prime radicalC23×D172C22
cosocleC22×C4×C43C24
hypercenterC2×#389D43
hypocenterC43C2×#1934
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#389

1462 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, 172172);