C₂₅×Dic₄₃ #16864316

order	4300
isoclinism	isoclinic class of D₄₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₅×Dic₄₃
unambiguous semidirect product	C₄₃⋊(C₄×C₂₅)

Splittings

derived, Sylow	C₄₃ ⋊ C₄×C₂₅
Hall	C₂₅×C₄₃ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₂₅	D₄₃
commutator, hypocenter	C₄₃	C₄×C₂₅
Frattini	C₂×C₅	C₅×D₄₃
Fitting	C₂×C₂₅×C₄₃	C₂
socle, prime radical, cosocle	C₂×C₅×C₄₃	C₂×C₅
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₂×C₂₅

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 72
transitive degree	μ_t(G) = 4300

A minimal faithful permutation representation — 2 generators on 72 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)(30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72);(26,28,27,29)(31,72)(32,71)(33,70)(34,69)(35,68)(36,67)(37,66)(38,65)(39,64)(40,63)(41,62)(42,61)(43,60)(44,59)(45,58)(46,57)(47,56)(48,55)(49,54)(50,53)(51,52)

Conjugacy classes & character table

1150 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₅×(C₄₃⋊C₃)⋊C₄, C₃×C₂₅×Dic₄₃, C₂₅×Dic₁₂₉, …
maximal normal subgroup of	C₂₅×(C₄₃⋊C₃)⋊C₄, C₃×C₂₅×Dic₄₃, C₇×C₂₅×Dic₄₃, …
maximal quotient of	C₃×C₂₅×Dic₄₃, C₂₅×Dic₁₂₉, C₇×C₂₅×Dic₄₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4300, 3);

C25×Dic43 #16864316