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C3×Dic74 #11725169

order888
isoclinismisoclinic class of Dic74
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic74

Splittings

HallC3×C37 ⋊ Q8
SylowC37 ⋊ C3×Q8

Subgroups

subgroupG/H
centerC2×C3C2×D37
commutator, cosocleC2×C37C22×C3
FrattiniC2C2×C3×D37
FittingC3×C4×C37C2
socle, prime radicalC2×C3×C37C22
hypercenterC3×C4D37
hypocenterC37C3×Q8
LCSG ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C3 ◁ C3×C4

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 48
transitive degreeμt(G) = 888

A minimal faithful permutation representation — 2 generators on 48 points:

(1,2,3)(4,5,6,7)(8,11,10,9)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48);(4,8,6,10)(5,9,7,11)(13,48)(14,47)(15,46)(16,45)(17,44)(18,43)(19,42)(20,41)(21,40)(22,39)(23,38)(24,37)(25,36)(26,35)(27,34)(28,33)(29,32)(30,31)

Conjugacy classes & character table

231 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13183828, #13183830, #13183833, …
maximal normal subgroup of#13183828, #13183830, #13183833, …
maximal quotient ofC3×#10596936, C3×C4⋊Dic37, C2×C3×Dic74

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(888, 27);