Finite Group Databasebeta

C2×#19147795 #26003192

order11008
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC2×#19147795

Splittings

FittingC2×C43×#520 ⋊ C2
SylowC43 ⋊ C2×#3428

Subgroups

subgroupG/H
centerC23C24×D43
commutatorC2×C43C25×C4
FrattiniC22C25×D43
FittingC2×C43×#520C2
socleC23×C43C25
prime radicalC22×#41×D43C2
cosocleC22×C43C26
hypercenterC2×#520D43
hypocenterC43C2×#3428
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#520

11534 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1564 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1076163);