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C3×C22⋊D23 #10587779

order552
isoclinismisoclinic class of Dic46
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×C22⋊D23

Splittings

FittingC22×C3×C23 ⋊ C2
HallC3×C23 ⋊ D4
SylowC23 ⋊ C3×D4

Subgroups

subgroupG/H
centerC2×C3C2×D23
commutator, cosocleC2×C23C22×C3
FrattiniC2C2×C3×D23
FittingC22×C3×C23C2
socleC2×C3×C23C22
hypercenterC22×C3D23
hypocenterC23C3×D4
LCSG ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C3 ◁ C22×C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 276

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

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

Conjugacy classes & character table

147 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11764236, #11764237, D3×C22⋊D23, …
maximal normal subgroup of#11764236, #11764237, D3×C22⋊D23, …
maximal quotient ofC3×Dic23⋊C4, C3×(C2×D23)⋊C4, C3×#67272, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(552, 17);