D₄₃×D₇₅ #27166357

order	12900
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

direct product	D₄₃×D₇₅
unambiguous semidirect product	(C₃×D₄₃)⋊D₂₅
unambiguous semidirect product	(C₂₅×D₄₃)⋊D₃

Splittings

Fitting, derived, Hall	C₃×C₂₅×C₄₃ ⋊ C₂²
Hall	C₂₅×C₄₃ ⋊ C₂×D₃
Hall	C₃×C₄₃ ⋊ C₂×D₂₅
Hall	C₃×C₂₅ ⋊ C₂×D₄₃
Sylow	C₄₃ ⋊ C₂×D₇₅
Sylow	C₂₅ ⋊ D₃×D₄₃
Sylow	C₃ ⋊ D₂₅×D₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×C₂₅×C₄₃	C₂²
Frattini	C₅	D₁₅×D₄₃
socle	C₃×C₅×C₄₃	C₂×D₅
LCS	G ▷ C₃×C₂₅×C₄₃
UCS	C₁

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 71
transitive degree	μ_t(G) = 3225

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12900, 26);

D43×D75 #27166357