Finite Group Databasebeta

C2×#19135581 #25101238

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

Aliases

direct productC2×#19135581

Splittings

SylowC43 ⋊ C2×#1996

Subgroups

subgroupG/H
centerC23C2×C22⋊Dic43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC22×C22⋊Q8×C43C2
socleC23×C43C2×C22⋊C4
prime radicalC25×C43C23
cosocleC24×C43C24
hypercenterC22×C22⋊Q8D43
hypocenterC43C2×#1996
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×C22⋊Q8

1698 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 174209);