C₂₅×Dic₂₀₁ #34117151

order	20100
automorphism	?
homology	Abelianization (H₁) = C₄×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₅×Dic₂₀₁
unambiguous semidirect product	C₃⋊(C₂₅×Dic₆₇)
unambiguous semidirect product	C₆₇⋊(Dic₃×C₂₅)

Splittings

derived, Hall	C₃×C₆₇ ⋊ C₄×C₂₅
Hall	C₃×C₂₅×C₆₇ ⋊ C₄
Hall	C₂₅×C₆₇ ⋊ Dic₃
Hall	C₃×C₂₅ ⋊ Dic₆₇
Sylow	C₆₇ ⋊ Dic₃×C₂₅
Sylow	C₃ ⋊ C₂₅×Dic₆₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₂₅	D₂₀₁
commutator, hypocenter	C₃×C₆₇	C₄×C₂₅
Frattini	C₂×C₅	C₅×D₂₀₁
Fitting	C₂×C₃×C₂₅×C₆₇	C₂
socle, prime radical, cosocle	C₂×C₃×C₅×C₆₇	C₂×C₅
LCS	G ▷ C₃×C₆₇
UCS	C₁ ◁ C₂×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)(69,70)(71,72,73,74)(75,76,78,81,85,77,79,82,86,90,80,83,87,91,94,84,88,92,95,97,89,93,96,98,99);(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)(68,69,70)

Conjugacy classes & character table

5100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20100, 7);

C25×Dic201 #34117151