C₃×D₂₅×D₆₇ #34117166

order	20100
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₃×D₂₅×D₆₇

Splittings

Fitting, Hall	C₃×C₂₅×C₆₇ ⋊ C₂²
derived, Hall	C₂₅×C₆₇ ⋊ C₂²×C₃
Hall	C₃×C₆₇ ⋊ C₂×D₂₅
Hall	C₃×C₂₅ ⋊ C₂×D₆₇
Sylow	C₆₇ ⋊ C₂×C₃×D₂₅
Sylow	C₂₅ ⋊ C₂×C₃×D₆₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₂₅×D₆₇
commutator, cosocle, hypocenter	C₂₅×C₆₇	C₂²×C₃
Frattini	C₅	C₃×D₅×D₆₇
Fitting	C₃×C₂₅×C₆₇	C₂²
socle	C₃×C₅×C₆₇	C₂×D₅
LCS	G ▷ C₂₅×C₆₇
UCS	C₁ ◁ C₃

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 95
transitive degree	μ_t(G) = 5025

A minimal faithful permutation representation — 2 generators on 95 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)(68,73,88,87,71,70,81,91,77,76,75,90,85,78,84,83,82,72,86,89,74,69,79,92,80)(93,94,95);(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)(69,71)(70,74)(72,77)(73,80)(75,83)(76,82)(78,85)(79,87)(81,89)(84,90)(86,91)(88,92)

Conjugacy classes & character table

1470 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20100, 22);

C3×D25×D67 #34117166