C₅²⋊C₃×Dic₄₃ #27166385

order	12900
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₅

Aliases

direct product

C₅²⋊C₃×Dic₄₃

Splittings

derived, Hall	C₅²×C₄₃ ⋊ C₃×C₄
Hall	C₅²×Dic₄₃ ⋊ C₃
Hall	C₄₃×C₅²⋊C₃ ⋊ C₄
Sylow	C₄₃ ⋊ C₄×C₅²⋊C₃
Sylow	C₅² ⋊ C₃×Dic₄₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₅²⋊C₃×D₄₃
commutator, hypocenter	C₅²×C₄₃	C₃×C₄
Fitting, socle, cosocle	C₂×C₅²×C₄₃	C₂×C₃
prime radical	C₂×C₄₃×C₅²⋊C₃	C₂
LCS	G ▷ C₅²×C₄₃
UCS	C₁ ◁ C₂

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 62
transitive degree	μ_t(G) = 2580

A minimal faithful permutation representation — 2 generators on 62 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)(44,45,47)(46,50,52)(48,53,56)(49,55,58)(51,54,57)(59,62,61,60);(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)(44,46,51,56,58)(45,50,54,48,49)(47,53,52,55,57)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12900, 54);

C52⋊C3×Dic43 #27166385