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Cayley diagram

C3×Dic31 #67311

order372
isoclinismisoclinic class of D31
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic31

Splittings

derived, SylowC31 ⋊ C3×C4
HallC3×C31 ⋊ C4

Subgroups

subgroupG/H
center, hypercenterC2×C3D31
commutator, hypocenterC31C3×C4
FrattiniC2C3×D31
Fitting, socle, prime radicalC2×C3×C31C2
cosocleC2×C31C2×C3
LCSG ▷ C31
UCSC1 ◁ C2×C3

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 38
transitive degreeμt(G) = 372

A minimal faithful permutation representation — 2 generators on 38 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);(4,6,5,7)(9,38)(10,37)(11,36)(12,35)(13,34)(14,33)(15,32)(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×Dic31, D93⋊C4, #10625226, …
maximal normal subgroup ofD3×Dic31, D93⋊C4, #10625226, …
maximal quotient ofC3×C31⋊C8, C2×C3×Dic31, C9×Dic31, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(372, 4);