#37551159

order	23226
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₇

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, Hall	C₇²×C₇₉ ⋊ C₂×C₃
Hall	C₇₉×#3862 ⋊ C₂
Hall	C₇⋊D₅₅₃ ⋊ C₃
Hall	#3862 ⋊ D₇₉
Sylow	C₇₉ ⋊ #64425
Sylow	C₇² ⋊ C₃×D₇₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²×C₇₉	C₂×C₃
LCS	G ▷ C₇²×C₇₉
UCS	C₁

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 93
transitive degree	μ_t(G) = 1659

A minimal faithful permutation representation — 2 generators on 93 points:

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

Polycyclic presentation:

2,3,7^2,79|c^a=c^6,d^a=d^6,e^a=e^78,c^b=c^2,d^b=d^4

Conjugacy classes & character table

755 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23226, 78);