C₂₅×D₄₃ #14524115

order	2150
isoclinism	isoclinic class of D₄₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

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

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂₅	D₄₃
commutator, hypocenter	C₄₃	C₂×C₂₅
Frattini	C₅	C₅×D₄₃
Fitting	C₂₅×C₄₃	C₂
socle, cosocle	C₅×C₄₃	C₂×C₅
prime radical	C₅×D₄₃	C₅
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₂₅

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 68
transitive degree	μ_t(G) = 1075

A minimal faithful permutation representation — 2 generators on 68 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₂₅×D₄₃, C₂×C₂₅×D₄₃, C₇×C₂₅×D₄₃, …
maximal normal subgroup of	D₂₅×D₄₃, C₂×C₂₅×D₄₃, C₇×C₂₅×D₄₃, …
maximal quotient of	C₂₅×Dic₄₃, C₂×C₂₅×D₄₃, C₇×C₂₅×D₄₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2150, 3);

C25×D43 #14524115