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C3×Dic44 #10587165

order528
isoclinismisoclinic class of #4314
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic44

Splittings

HallC3×C11 ⋊ Q16
SylowC11 ⋊ C3×Q16

Subgroups

subgroupG/H
centerC2×C3D44
commutator, cosocleC4×C11C22×C3
FrattiniC4C2×C3×D11
FittingC3×C8×C11C2
socle, prime radicalC2×C3×C11D4
hypercenterC3×C8D11
hypocenterC11C3×Q16
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 528

A minimal faithful permutation representation — 2 generators on 30 points:

(1,2,3)(4,5,6,7,8,9,10,11)(12,19,18,17,16,15,14,13)(20,21,22,23,24,25,26,27,28,29,30);(4,12,8,16)(5,13,9,17)(6,14,10,18)(7,15,11,19)(21,30)(22,29)(23,28)(24,27)(25,26)

Conjugacy classes & character table

141 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11760478, #11760480, #11760483, …
maximal normal subgroup of#11760478, #11760480, #11760483, …
maximal quotient ofC3×#66882, C3×#66880, C2×C3×Dic44, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(528, 35);