C₂×C₂₅×D₁₂₉ #27166369

order	12900
isoclinism	isoclinic class of D₁₂₉
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₂₅×D₁₂₉
unambiguous semidirect product	(C₂×C₃)⋊(C₂₅×D₄₃)
unambiguous semidirect product	(C₂×C₄₃)⋊(D₃×C₂₅)

Splittings

Fitting	C₂×C₃×C₂₅×C₄₃ ⋊ C₂
derived, Hall	C₃×C₄₃ ⋊ C₂²×C₂₅
Hall	C₃×C₂₅×C₄₃ ⋊ C₂²
Hall	C₂₅×C₄₃ ⋊ C₂×D₃
Hall	C₃×C₂₅ ⋊ C₂×D₄₃
Sylow	C₄₃ ⋊ C₂×D₃×C₂₅
Sylow	C₃ ⋊ C₂×C₂₅×D₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₂₅	D₁₂₉
commutator, hypocenter	C₃×C₄₃	C₂²×C₂₅
Frattini	C₅	C₂×C₅×D₁₂₉
Fitting	C₂×C₃×C₂₅×C₄₃	C₂
socle	C₂×C₃×C₅×C₄₃	C₂×C₅
prime radical	C₂×C₅×D₁₂₉	C₅
cosocle	C₃×C₅×C₄₃	C₂²×C₅
LCS	G ▷ C₃×C₄₃
UCS	C₁ ◁ C₂×C₂₅

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:

(2,3)(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)(45,46)(47,51,59,67,71,49,55,64,70,57,52,60,68,53,62,56,65,50,58,66,61,48,54,63,69);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(44,45,46)(72,73)

Conjugacy classes & character table

3300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12900, 38);

C2×C25×D129 #27166369