Finite Group Databasebeta

C2×#19136308 #25249496

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#19136308

Splittings

FittingC22×M32×C43 ⋊ C2
SylowC43 ⋊ C2×#2139

Subgroups

subgroupG/H
centerC23C2×D344
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC22×M32×C43C2
socleC23×C43C2×D8
prime radicalC22×#13063347C2
cosocleC2×C8×C43C24
hypercenterC22×M32D43
hypocenterC43C2×#2139
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C22×M32

1214 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1744 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322467);