Finite Group Databasebeta

C2×#19135028 #25098279

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#19135028

Splittings

SylowC43 ⋊ C2×#1894

Subgroups

subgroupG/H
centerC24C2×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC23×M16×C43C2
socleC24×C43C2×D4
prime radicalC25×C43D4
cosocleC22×C4×C43C24
hypercenterC23×M16D43
hypocenterC43C2×#1894
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C24×C4 ◁ C23×M16

1966 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, 171250);