Finite Group Databasebeta

#117×C22⋊D43 #25255997

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4

Aliases

direct product#117×C22⋊D43

Splittings

FittingC22×#117×C43 ⋊ C2
SylowC43 ⋊ D4×#117

Subgroups

subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC22×#117×C43C2
socle, cosocleC23×C43C25
prime radicalC23×C22⋊D43C22
hypercenterC22×#117D43
hypocenterC43D4×#117
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C22×#117

3562 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 328968);