Finite Group Databasebeta

C42×#10621884 #25095069

order11008
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC42×#10621884

Splittings

FittingC42×Q8×C43 ⋊ C2
SylowC43 ⋊ C42×SD16

Subgroups

subgroupG/H
centerC2×C42C22⋊D43
commutatorC4×C43C22×C42
FrattiniC22×C4C23×D43
FittingC42×Q8×C43C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenterC42×Q8D43
hypocenterC43C42×SD16
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C42 ◁ C43 ◁ C42×Q8

1230 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1792 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 168040);