#49181577

order	37926
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Splittings

derived, Hall	C₇²×C₄₃ ⋊ C₂×C₉
Hall	C₇×#14582150 ⋊ C₂
Hall	C₇⋊D₃₀₁ ⋊ C₉
Sylow	C₇² ⋊ D₄₃⋊C₉
Sylow	C₄₃ ⋊ (C₇⋊C₉)⋊D₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₃	#27162427
commutator, hypocenter	C₇²×C₄₃	C₂×C₉
Fitting, socle, cosocle	C₃×C₇²×C₄₃	C₂×C₃
prime radical	C₃×C₇⋊D₃₀₁	C₃
LCS	G ▷ C₇²×C₄₃
UCS	C₁ ◁ C₃

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 66
transitive degree	μ_t(G) = 2709

A minimal faithful permutation representation — 2 generators on 66 points:

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

Polycyclic presentation:

2,3,7^2,43,3|b^3=f,c^a=c^6,d^a=d^6,e^a=e^42,c^b=c^2,e^b=e^6

Conjugacy classes & character table

1095 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37926, 150);