C₈₃×#3874 #27159484

order	12450
isoclinism	isoclinic class of #3874
automorphism	?
homology	Abelianization (H₁) = C₂×C₈₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₈₃×#3874

Splittings

Fitting, socle, Hall	C₅²×C₈₃ ⋊ D₃
derived, Hall	C₅²⋊C₃ ⋊ C₂×C₈₃
Hall	C₅²⋊C₃×C₈₃ ⋊ C₂
Sylow	C₅² ⋊ D₃×C₈₃

Subgroups

	subgroup	G/H
center, hypercenter	C₈₃	#3874
commutator, cosocle, hypocenter	C₅²⋊C₃	C₂×C₈₃
Frattini	C₁	G
Fitting, socle	C₅²×C₈₃	D₃
LCS	G ▷ C₅²⋊C₃
UCS	C₁ ◁ C₈₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 98
transitive degree	μ_t(G) = 1245

A minimal faithful permutation representation — 2 generators on 98 points:

(1,7)(2,4,6,13,5,9,12,10,11,14)(3,15)(16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98);(1,2,4)(3,6,14)(5,10,8)(7,11,13)(9,15,12)

Conjugacy classes & character table

1079 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₈₃×#3874⋊C₂, #3874⋊D₈₃, #3874×D₈₃, …
maximal normal subgroup of	C₈₃×#3874⋊C₂, #3874⋊D₈₃, #3874×D₈₃, …
maximal quotient of	C₈₃×#64470, C₂×C₈₃×#3874, C₈₃×#90646, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12450, 10);

C83×#3874 #27159484