C₃²×C₅×Dic₇₃ #27190232

order	13140
isoclinism	isoclinic class of D₇₃
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄×C₅ · Schur multiplier (H₂) = C₃

Aliases

direct product

C₃²×C₅×Dic₇₃

Splittings

derived, Sylow	C₇₃ ⋊ C₃²×C₄×C₅
Hall	C₃²×C₅×C₇₃ ⋊ C₄
Hall	C₃²×C₇₃ ⋊ C₄×C₅
Hall	C₅×C₇₃ ⋊ C₃²×C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₅	D₇₃
commutator, hypocenter	C₇₃	C₃²×C₄×C₅
Frattini	C₂	C₃²×C₅×D₇₃
Fitting, socle, prime radical	C₂×C₃²×C₅×C₇₃	C₂
cosocle	C₂×C₇₃	C₂×C₃²×C₅
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₂×C₃²×C₅

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 88
transitive degree	μ_t(G) = 13140

A minimal faithful permutation representation — 2 generators on 88 points:

(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)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,77,76,75)(78,79,80,81,82)(86,87,88);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(83,84,85)

Conjugacy classes & character table

3420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13140, 66);

C32×C5×Dic73 #27190232