Finite Group Databasebeta

C22×#63578 #11858623

order1152
isoclinismisoclinic class of #3713
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC22×#63578

Splittings

SylowC32 ⋊ C22×#108

Subgroups

subgroupG/H
centerC22×C4#625
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C4⋊C4
prime radicalC24×C32Q8
cosocleC2×C32×C4C24
hypercenterC23×C4D32
hypocenterC32C22×#108
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

1129 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 92634);