Finite Group Databasebeta

C2×#19135435 #25100361

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

Aliases

direct productC2×#19135435

Splittings

FittingC2×C4×M16×C43 ⋊ C2
SylowC43 ⋊ C2×#1965

Subgroups

subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C4×M16×C43C2
socleC23×C43C2×C22⋊C4
prime radicalC22×#13063322C2
cosocleC22×C4×C43C24
hypercenterC2×C4×M16D43
hypocenterC43C2×#1965
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×M16

2206 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, 173332);