Finite Group Databasebeta

C2×#19134687 #25096375

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

Aliases

direct productC2×#19134687

Splittings

SylowC43 ⋊ C2×#1825

Subgroups

subgroupG/H
centerC24C2×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#380C2
socleC24×C43C2×D4
prime radicalC25×C43D4
cosocleC22×C4×C43C24
hypercenterC2×#380D43
hypocenterC43C2×#1825
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C24×C4 ◁ C2×#380

1574 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1252 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 169346);