Finite Group Databasebeta

C2×#19136737 #25251220

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

direct productC2×#19136737

Splittings

SylowC43 ⋊ C2×#2225

Subgroups

subgroupG/H
centerC23C2×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC2×C4×Q16×C43C2
socle, prime radicalC23×C43C2×D8
hypercenterC2×C4×Q16D43
hypocenterC43C2×#2225
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×Q16

574 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1234 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 324191);