Finite Group Databasebeta

C2×#19134753 #25096997

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

Aliases

direct productC2×#19134753

Splittings

SylowC43 ⋊ C2×#1845

Subgroups

subgroupG/H
centerC24D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×#107×C43C2
socle, prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenterC22×#107D43
hypocenterC43C2×#1845
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#107

1358 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, 169968);