Finite Group Databasebeta

C2×#19135500 #25100585

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

Aliases

direct productC2×#19135500

Splittings

SylowC43 ⋊ C2×#1977

Subgroups

subgroupG/H
centerC23#13063296
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC23×SD16×C43C2
socleC23×C43#121
prime radicalC23×D4×C43C22
cosocleC22×C4×C43C24
hypercenterC23×SD16D43
hypocenterC43C2×#1977
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×SD16

1566 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, 173556);