C₂×C₃×C₄₃×D₂₅ #27166366

order	12900
isoclinism	isoclinic class of D₂₅
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₄₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₃×C₄₃×D₂₅
unambiguous semidirect product	C₂₅⋊(C₂²×C₃×C₄₃)
unambiguous semidirect product	(C₂×C₂₅)⋊(C₂×C₃×C₄₃)

Splittings

Fitting	C₂×C₃×C₂₅×C₄₃ ⋊ C₂
derived, Sylow	C₂₅ ⋊ C₂²×C₃×C₄₃
Hall	C₃×C₂₅×C₄₃ ⋊ C₂²
Hall	C₂₅×C₄₃ ⋊ C₂²×C₃
Hall	C₃×C₂₅ ⋊ C₂²×C₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₄₃	D₂₅
commutator, cosocle, hypocenter	C₂₅	C₂²×C₃×C₄₃
Frattini	C₅	C₂×C₃×D₅×C₄₃
Fitting	C₂×C₃×C₂₅×C₄₃	C₂
socle	C₂×C₃×C₅×C₄₃	D₅
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₂×C₃×C₄₃

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 6450

A minimal faithful permutation representation — 2 generators on 73 points:

(2,4)(3,7)(5,10)(6,13)(8,16)(9,15)(11,18)(12,20)(14,22)(17,23)(19,24)(21,25)(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);(1,6,21,20,4,3,14,24,10,9,8,23,18,11,17,16,15,5,19,22,7,2,12,25,13)(72,73)

Conjugacy classes & character table

3612 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12900, 35);

C2×C3×C43×D25 #27166366