C₂₅×D₆₇ #16809772

order	3350
isoclinism	isoclinic class of D₆₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₅×D₆₇
unambiguous semidirect product	C₆₇⋊(C₂×C₂₅)

Splittings

Fitting, Hall	C₂₅×C₆₇ ⋊ C₂
derived, Sylow	C₆₇ ⋊ C₂×C₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂₅	D₆₇
commutator, hypocenter	C₆₇	C₂×C₂₅
Frattini	C₅	C₅×D₆₇
Fitting	C₂₅×C₆₇	C₂
socle, cosocle	C₅×C₆₇	C₂×C₅
prime radical	C₅×D₆₇	C₅
LCS	G ▷ C₆₇
UCS	C₁ ◁ C₂₅

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 92
transitive degree	μ_t(G) = 1675

A minimal faithful permutation representation — 2 generators on 92 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)(26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92);(27,92)(28,91)(29,90)(30,89)(31,88)(32,87)(33,86)(34,85)(35,84)(36,83)(37,82)(38,81)(39,80)(40,79)(41,78)(42,77)(43,76)(44,75)(45,74)(46,73)(47,72)(48,71)(49,70)(50,69)(51,68)(52,67)(53,66)(54,65)(55,64)(56,63)(57,62)(58,61)(59,60)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₇×C₂₅×D₆₇, C₂₅×D₄₆₉, C₁₁×C₂₅×D₆₇, …
maximal normal subgroup of	C₇×C₂₅×D₆₇, C₁₁×C₂₅×D₆₇, C₂₅×D₆₇⋊C₁₁
maximal quotient of	C₇×C₂₅×D₆₇, C₂₅×D₄₆₉, C₁₁×C₂₅×D₆₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3350, 3);

C25×D67 #16809772