Finite Group Databasebeta

C2×#19136360 #25249596

order11008
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#19136360

Splittings

SylowC43 ⋊ C2×#2153

Subgroups

subgroupG/H
centerC2×C8C2×C22⋊D43
commutatorC4×C43C23×C8
FrattiniC2×C8C23×D43
FittingC22×M32×C43C2
socleC22×C43C2×C4⋊C8
prime radicalC24×C43M16
cosocleC2×C8×C43C24
hypercenterC22×M32D43
hypocenterC43C2×#2153
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C8 ◁ C23×C8 ◁ C22×M32

698 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322567);