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C3×Dic62 #10625233

order744
isoclinismisoclinic class of Dic62
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic62

Splittings

HallC3×C31 ⋊ Q8
SylowC31 ⋊ C3×Q8

Subgroups

subgroupG/H
centerC2×C3C2×D31
commutator, cosocleC2×C31C22×C3
FrattiniC2C2×C3×D31
FittingC3×C4×C31C2
socle, prime radicalC2×C3×C31C22
hypercenterC3×C4D31
hypocenterC31C3×Q8
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C3 ◁ C3×C4

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 42
transitive degreeμt(G) = 744

A minimal faithful permutation representation — 2 generators on 42 points:

(1,2,3)(4,5,6,7)(8,11,10,9)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42);(4,8,6,10)(5,9,7,11)(13,42)(14,41)(15,40)(16,39)(17,38)(18,37)(19,36)(20,35)(21,34)(22,33)(23,32)(24,31)(25,30)(26,29)(27,28)

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13093437, #13093439, #13093442, …
maximal normal subgroup of#13093437, #13093439, #13093442, …
maximal quotient ofC3×Dic31⋊C4, C3×C4⋊Dic31, C2×C3×Dic62

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(744, 24);