Finite Group Databasebeta

C2×#19136311 #25249484

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

Aliases

direct productC2×#19136311

Splittings

SylowC43 ⋊ C2×#2140

Subgroups

subgroupG/H
centerC23C2×#10621882
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
Fitting, prime radicalC23×D8×C43C2
socleC23×C43C2×D8
cosocleC2×C8×C43C24
hypercenterC23×D8D43
hypocenterC43C2×#2140
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C23×D8

1406 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322455);