Finite Group Databasebeta

C2×#19136249 #25249334

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

Aliases

direct productC2×#19136249

Splittings

SylowC43 ⋊ C2×#2123

Subgroups

subgroupG/H
centerC22C2×#13063240
commutatorC23×C43C23×C4
FrattiniC2×D4C23×D43
FittingC2×C43×#536C2
socleC22×C43C2×#99
prime radicalC22×#41×C43C22
cosocleC2×D4×C43C24
hypercenterC2×#536D43
hypocenterC43C2×#2123
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ C2×#536

1214 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

970 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322305);