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C3×D148 #11725171

order888
isoclinismisoclinic class of Dic74
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×D148
unambiguous semidirect productC4⋊(C3×D37)

Splittings

FittingC3×C4×C37 ⋊ C2
HallC3×C37 ⋊ D4
SylowC37 ⋊ C3×D4

Subgroups

subgroupG/H
centerC2×C3C2×D37
commutator, cosocleC2×C37C22×C3
FrattiniC2C2×C3×D37
FittingC3×C4×C37C2
socleC2×C3×C37C22
hypercenterC3×C4D37
hypocenterC37C3×D4
LCSG ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C3 ◁ C3×C4

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 44
transitive degreeμt(G) = 444

A minimal faithful permutation representation — 2 generators on 44 points:

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

Conjugacy classes & character table

231 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13183824, #13183825, #13183827, …
maximal normal subgroup of#13183824, #13183825, #13183827, …
maximal quotient ofC3×#10596930, C3×D296, C3×Dic148, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(888, 29);