Finite Group Databasebeta

C2×#19134630 #25096208

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#19134630

Splittings

FittingC22×#108×C43 ⋊ C2
SylowC43 ⋊ C2×#1810

Subgroups

subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×#108×C43C2
socleC23×C43C2×C4⋊C4
prime radicalC24×D43Q8
cosocleC22×C4×C43C24
hypercenterC22×#108D43
hypocenterC43C2×#1810
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#108

1566 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1264 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 169179);