#27211344

order	13359
automorphism	?
homology	Abelianization (H₁) = C₃ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, Hall	C₆₁×C₇₃ ⋊ C₃
Sylow	C₇₃ ⋊ C₆₁⋊C₃
Sylow	C₆₁ ⋊ C₇₃⋊C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₆₁×C₇₃	C₃
LCS	G ▷ C₆₁×C₇₃
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 134
transitive degree	μ_t(G) = 4453

A minimal faithful permutation representation — 2 generators on 134 points:

(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,35)(18,27,32)(21,30,29)(23,33,26)(25,37,50)(28,40,47)(31,38,44)(34,45,42)(36,48,39)(41,53,62)(43,54,59)(46,58,57)(49,60,55)(51,63,52)(56,66,69)(61,68,67)(64,70,65)(71,73,72)(75,76,78)(77,80,85)(79,83,82)(81,87,95)(84,90,92)(86,93,89)(88,97,107)(91,99,104)(94,102,101)(96,105,98)(100,110,117)(103,112,114)(106,115,111)(108,118,109)(113,121,125)(116,123,122)(119,126,120)(124,129,130)(127,131,128)(132,134,133);(1,2,4,8,15,25,38,17,3,6,11,18,28,41,54,27,7,13,21,31,43,56,66,40,14,23,34,46,50,62,69,53,24,36,49,61,63,35,47,59,37,51,64,71,70,48,22,32,44,57,67,72,73,60,33,12,19,29,42,55,65,68,45,20,5,9,16,26,39,52,58,30,10)(74,75,77,81,88,97,108,119,127,132,131,115,93,78,82,89,98,109,110,87,96,106,116,124,126,105,85,92,101,111,120,121,99,80,86,94,103,113,118,95,104,114,122,128,129,112,90,76,79,84,91,100,107,117,125,130,133,134,123,102,83)

Polycyclic presentation:

3,61,73|b^a=b^47,c^a=c^8

Conjugacy classes & character table

1487 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×#27211344, #40999132, #40999136, …
maximal normal subgroup of	C₂×#27211344, #40999132, #40999136, …
maximal quotient of	C₂×#27211344

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13359, 4);