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C3×#4318 #10587167

order528
isoclinismisoclinic class of Dic22
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×#4318

Splittings

HallC3×C11 ⋊ M16
SylowC11 ⋊ C3×M16

Subgroups

subgroupG/H
centerC3×C4C2×D11
commutatorC2×C11C2×C3×C4
FrattiniC4C2×C3×D11
FittingC2×C3×C4×C11C2
socleC2×C3×C11C2×C4
prime radicalC22×C3×C11C4
cosocleC4×C11C22×C3
hypercenterC2×C3×C4D11
hypocenterC11C3×M16
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C3×C4 ◁ C2×C3×C4

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 22
transitive degreeμt(G) = 264

A minimal faithful permutation representation — 2 generators on 22 points:

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

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11760496, #11760497, #11760499, …
maximal normal subgroup of#11760496, #11760497, #11760499, …
maximal quotient ofC3×#66867, C3×C4⋊(C11⋊C8), C3×C22⋊(C11⋊C8), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(528, 37);