Finite Group Databasebeta

#120×C43⋊C8 #25102093

order11008
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct product#120×C43⋊C8

Splittings

SylowC43 ⋊ C8×#120

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D43
commutatorC22×C43C23×C8
FittingC4×#120×C43C2
socleC23×C43C23×C4
prime radicalC2×#120×C43C4
cosocleC22×C4×C43C24
hypercenterC4×#120D43
hypocenterC43C8×#120
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C4×#120

1786 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1288 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 175064);