Finite Group Databasebeta

C2×#19136345 #25249559

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

Aliases

direct productC2×#19136345

Splittings

FittingC22×M32×C43 ⋊ C2
SylowC43 ⋊ C2×#2148

Subgroups

subgroupG/H
centerC2×C4#13063247
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC22×M32×C43C2
socleC22×C43C2×#102
prime radicalC22×#13063347C2
cosocleC2×C8×C43C24
hypercenterC22×M32D43
hypocenterC43C2×#2148
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8 ◁ C22×M32

1154 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, 322530);