D₂₅×C₆₇ #16809771

order	3350
isoclinism	isoclinic class of D₂₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₆₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₂₅×C₆₇
unambiguous semidirect product	C₂₅⋊(C₂×C₆₇)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₆₇	D₂₅
commutator, cosocle, hypocenter	C₂₅	C₂×C₆₇
Frattini	C₅	D₅×C₆₇
Fitting	C₂₅×C₆₇	C₂
socle	C₅×C₆₇	D₅
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₆₇

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);(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₇×D₂₅×C₆₇, C₆₇×D₁₇₅, C₁₁×D₂₅×C₆₇, …
maximal normal subgroup of	C₇×D₂₅×C₆₇, C₁₁×D₂₅×C₆₇, D₂₅×C₆₇⋊C₁₁
maximal quotient of	C₇×D₂₅×C₆₇, C₆₇×D₁₇₅, C₁₁×D₂₅×C₆₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3350, 2);

D25×C67 #16809771