C₂×C₄₃×D₇₅ #27166370

order	12900
isoclinism	isoclinic class of D₇₅
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₄₃×D₇₅
unambiguous semidirect product	(C₂×C₃)⋊(C₄₃×D₂₅)
unambiguous semidirect product	(C₂×C₂₅)⋊(D₃×C₄₃)

Splittings

Fitting	C₂×C₃×C₂₅×C₄₃ ⋊ C₂
derived, Hall	C₃×C₂₅ ⋊ C₂²×C₄₃
Hall	C₃×C₂₅×C₄₃ ⋊ C₂²
Hall	C₂₅×C₄₃ ⋊ C₂×D₃
Hall	C₃×C₄₃ ⋊ C₂×D₂₅
Sylow	C₂₅ ⋊ C₂×D₃×C₄₃
Sylow	C₃ ⋊ C₂×C₄₃×D₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄₃	D₇₅
commutator, cosocle, hypocenter	C₃×C₂₅	C₂²×C₄₃
Frattini	C₅	C₂×D₁₅×C₄₃
Fitting	C₂×C₃×C₂₅×C₄₃	C₂
socle	C₂×C₃×C₅×C₄₃	D₅
LCS	G ▷ C₃×C₂₅
UCS	C₁ ◁ C₂×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)(11,12)(14,20)(17,21)(18,22)(19,24)(23,25)(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);(1,21,12,24,9,7,14,5,23,4,16,6,22,18,13,8,2,25,10,20,3,15,19,11,17)(26,27,28)(72,73)

Conjugacy classes & character table

3354 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12900, 39);

C2×C43×D75 #27166370