Finite Group Databasebeta

C22×(C2×D43)⋊C16 #25249261

order11008
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C27

Aliases

direct productC22×(C2×D43)⋊C16

Splittings

FittingC23×C16×C43 ⋊ C2
SylowC43 ⋊ C22×C22⋊C16

Subgroups

subgroupG/H
centerC23×C8C2×D43
commutatorC2×C43C23×C16
FrattiniC2×C8C23×D43
FittingC23×C16×C43C2
socleC24×C43C2×C8
prime radicalC24×D43C8
cosocleC2×C8×C43C24
hypercenterC23×C16D43
hypocenterC43C22×C22⋊C16
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C23×C8 ◁ C23×C16

1470 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2848 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322232);