C₇₃×#33827 #32943231

order	18688
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₇₃×#33827

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₇₃
prime radical	C₂³×C₇₃	C₂×D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ #117×C₇₃ ◁ #405×C₇₃ ◁ G

464 conjugacy classes of subgroups; only the 194 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 194 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 145
transitive degree	μ_t(G) = 9344

A minimal faithful permutation representation — 4 generators on 145 points:

(2,5)(3,7)(9,10,15,20)(11,16,22,37)(12,25,28,59)(13,29,33,58)(14,34,31,19)(17,40,42,26)(18,43,45,32)(21,47,48,70)(23,53,51,69)(24,56,52,39)(27,60,35,44)(30,46,61,41)(36,62,63,49)(38,66,65,55)(50,71,57,67)(54,68,72,64)(73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145);(1,2)(3,6)(4,5)(7,8)(9,11,15,22)(10,16,20,37)(12,21,28,48)(13,23,33,51)(14,24,31,52)(17,36,42,63)(18,38,45,65)(19,39,34,56)(25,47,59,70)(26,49,40,62)(27,50,35,57)(29,53,58,69)(30,54,61,72)(32,55,43,66)(41,64,46,68)(44,67,60,71);(2,5)(6,8)(9,12,15,28)(10,17,20,42)(11,21,22,48)(13,30,33,61)(14,35,31,27)(16,36,37,63)(18,44,45,60)(19,46,34,41)(23,54,51,72)(24,57,52,50)(25,58,59,29)(26,43,40,32)(38,67,65,71)(39,68,56,64)(47,69,70,53)(49,66,62,55);(1,3,4,7)(2,6,5,8)(11,22)(16,37)(21,48)(23,51)(24,52)(36,63)(38,65)(39,56)(47,70)(49,62)(50,57)(53,69)(54,72)(55,66)(64,68)(67,71)

Conjugacy classes & character table

2920 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 26815);