C₃×C₂₅×Dic₆₇ #34117147

order	20100
isoclinism	isoclinic class of D₆₇
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×C₂₅×Dic₆₇

Splittings

derived, Sylow	C₆₇ ⋊ C₃×C₄×C₂₅
Hall	C₃×C₂₅×C₆₇ ⋊ C₄
Hall	C₂₅×C₆₇ ⋊ C₃×C₄
Hall	C₃×C₆₇ ⋊ C₄×C₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₂₅	D₆₇
commutator, hypocenter	C₆₇	C₃×C₄×C₂₅
Frattini	C₂×C₅	C₃×C₅×D₆₇
Fitting	C₂×C₃×C₂₅×C₆₇	C₂
socle, prime radical	C₂×C₃×C₅×C₆₇	C₂×C₅
cosocle	C₂×C₅×C₆₇	C₂×C₃×C₅
LCS	G ▷ C₆₇
UCS	C₁ ◁ C₂×C₃×C₂₅

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 99
transitive degree	μ_t(G) = 20100

A minimal faithful permutation representation — 2 generators on 99 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)(68,71,70,69)(72,76,84,92,96,74,80,89,95,82,77,85,93,78,87,81,90,75,83,91,86,73,79,88,94)(97,98,99);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)

Conjugacy classes & character table

5250 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20100, 3);

C3×C25×Dic67 #34117147