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C32×#3532 #11770581

order1152
nilpotency class2
isoclinismisoclinic class of #3532
automorphism?
homologyAbelianization (H1) = C25×C32 · Schur multiplier (H2) = C28×C3

Aliases

direct productC32×#3532

Subgroups

subgroupG/H
center, socleC22×C32C25
commutator, Frattini, cosocleC22C25×C32
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C32 ◁ G

4008 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 22
transitive degreeμt(G) = 144

A minimal faithful permutation representation — 5 generators on 22 points:

(1,2,3)(7,8)(9,15)(10,14)(11,13)(12,17)(16,19)(18,21)(20,22);(4,5,6)(7,9)(8,12)(10,17)(11,16)(13,20)(14,15)(18,22)(19,21);(8,13)(9,16)(14,21)(17,22);(8,13)(9,17)(12,19)(14,21)(15,20)(16,22);(8,14)(12,15)(13,21)(19,20)

Conjugacy classes & character table

342 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC32×#62817
maximal normal subgroup ofC32×#62817

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 4592);