Finite Group Databasebeta

C42×#10621902 #25254797

order11008
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC42×#10621902

Splittings

FittingC42×Q8×C43 ⋊ C2
SylowC43 ⋊ C42×#41

Subgroups

subgroupG/H
centerC2×C42C22×D43
commutatorC2×C43C23×C42
FrattiniC23C24×D43
FittingC42×Q8×C43C2
socle, cosocleC23×C43C25
prime radicalC22×#10621902C22
hypercenterC42×Q8D43
hypocenterC43C42×#41
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C42 ◁ C42×Q8

4086 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 327768);