#45681971

order	32946
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁₇

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, Hall	C₁₇²×C₁₉ ⋊ C₂×C₃
Hall	C₁₉×C₁₇²⋊C₃ ⋊ C₂
Hall	C₁₇⋊D₃₂₃ ⋊ C₃
Hall	C₁₇²⋊C₃ ⋊ D₁₉
Sylow	C₁₇² ⋊ C₃×D₁₉
Sylow	C₁₉ ⋊ (C₁₇⋊D₁₇)⋊C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₇²×C₁₉	C₂×C₃
LCS	G ▷ C₁₇²×C₁₉
UCS	C₁

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 70
transitive degree	μ_t(G) = 969

A minimal faithful permutation representation — 2 generators on 70 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21,23)(22,38,39,26,27,51)(24,48,50,31,32,43)(25,30,56,35,36,46)(28,40,29,42,34,44)(33,61,67,41,53,68)(37,47,69,54,57,64)(45,63,59,60,62,58)(49,52,70,55,65,66);(1,2,4,6,8,10,12,14,16,18,19,17,15,13,11,9,7,5,3)(20,22,28,43,62,56,68,64,70,66,69,67,46,63,50,42,26)(21,24,33,49,25,34,38,58,37,54,59,27,40,35,55,41,31)(23,29,45,61,65,57,30,32,51,39,48,36,47,52,53,60,44)

Polycyclic presentation:

2,3,17^2,19|c^a=c^16,d^a=d^16,e^a=e^18,c^b=c^2d^15,d^b=c^12d^14

Conjugacy classes & character table

945 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32946, 21);