Finite Group Databasebeta

C2×#19132909 #25062391

order11008
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#19132909

Splittings

SylowC43 ⋊ C2×#1458

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic43
commutatorC22×C43C23×C8
FrattiniC22×C4C23×D43
FittingC22×#117×C43C2
socleC23×C43C2×C22⋊C4
prime radicalC25×C43C2×C4
cosocleC22×C4×C43C24
hypercenterC22×#117D43
hypocenterC43C2×#1458
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×#117

1390 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, 135362);