Finite Group Databasebeta

C2×#19134537 #25095839

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#19134537

Splittings

FittingC22×#104×C43 ⋊ C2
SylowC43 ⋊ C2×#1789

Subgroups

subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×#104×C43C2
socleC23×C43C2×C22⋊C4
prime radicalC22×#41×D43C2
cosocleC22×C4×C43C24
hypercenterC22×#104D43
hypocenterC43C2×#1789
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#104

4102 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, 168810);