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C23×#67 #10587784

order552
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C22×C23 · Schur multiplier (H2) = C2

Aliases

direct productC23×#67

Splittings

FittingC22×C3×C23 ⋊ C2
HallC3×C23 ⋊ D4
SylowC3 ⋊ D4×C23

Subgroups

subgroupG/H
centerC2×C23C2×D3
commutator, cosocleC2×C3C22×C23
FrattiniC2C2×D3×C23
FittingC22×C3×C23C2
socleC2×C3×C23C22
hypercenterC22×C23D3
hypocenterC3D4×C23
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C23 ◁ C22×C23

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:

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

Conjugacy classes & character table

207 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11764237, #11764239, #67×D23, …
maximal normal subgroup of#11764237, #11764239, #67×D23, …
maximal quotient ofC23×Dic3⋊C4, C23×(C2×D3)⋊C4, C23×#213, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(552, 22);