C₂²×C₂₅×C₄₃⋊C₃ #27166362

order	12900
isoclinism	isoclinic class of C₄₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₂₅ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂²×C₂₅×C₄₃⋊C₃

Splittings

Fitting, Hall	C₂²×C₂₅×C₄₃ ⋊ C₃
derived, Sylow	C₄₃ ⋊ C₂²×C₃×C₂₅
Hall	C₂₅×C₄₃ ⋊ C₂²×C₃
Hall	C₂²×C₄₃ ⋊ C₃×C₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂²×C₂₅	C₄₃⋊C₃
commutator, hypocenter	C₄₃	C₂²×C₃×C₂₅
Frattini	C₅	C₂²×C₅×C₄₃⋊C₃
Fitting	C₂²×C₂₅×C₄₃	C₃
socle	C₂²×C₅×C₄₃	C₃×C₅
prime radical	C₂²×C₅×C₄₃⋊C₃	C₅
cosocle	C₅×C₄₃	C₂²×C₃×C₅
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₂²×C₂₅

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 72
transitive degree	μ_t(G) = 4300

A minimal faithful permutation representation — 2 generators on 72 points:

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

Conjugacy classes & character table

1700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12900, 31);

C22×C25×C43⋊C3 #27166362