#72209948

order	29160
isoclinism	isoclinic class of #72209948
automorphism	?
homology	Abelianization (H₁) = C₁ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Frattini, socle, hypercenter	C₂×C₃	#72209608
commutator, hypocenter	G	C₁
Fitting, cosocle	C₂×C₃⁵	A₅
LCS	G
UCS	C₁ ◁ C₂×C₃

573 conjugacy classes of subgroups; only the 7 normal subgroups are shown.

normal subgroups only

This group has 573 conjugacy classes of subgroups — too many to draw. Only its 7 normal subgroups are shown.

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

Full subgroup data →

Presentation

Permutation generators:

(1,2,5,3)(4,7,6,8)(9,13,11,14)(10,15,12,16)(17,19,18,20)(21,24,23,22)(25,26)(27,32)(28,31)(29,30)(33,38)(34,37);(1,4,2)(3,5,6)(7,9,10)(8,11,12)(13,16,17)(14,15,18)(19,21,22)(20,23,24)(25,27,26)(28,34,31)(29,33,30)(32,35,36)(37,40,41)(38,39,42);(25,28,29)(26,30,31)(27,33,34)(36,41,42);(25,29,28)(26,30,31)(27,34,33)(32,37,38);(25,28,29)(27,34,33)(32,38,37)(36,42,41);(25,29,28)(26,31,30)(32,38,37)(36,41,42);(25,29,28)(26,30,31)(27,33,34)(32,38,37)(35,39,40)(36,42,41)

Conjugacy classes & character table

87 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:

gap> G := Group((1,2,5,3)(4,7,6,8)(9,13,11,14)(10,15,12,16)(17,19,18,20)(21,24,23,22)(25,26)(27,32)(28,31)(29,30)(33,38)(34,37), (1,4,2)(3,5,6)(7,9,10)(8,11,12)(13,16,17)(14,15,18)(19,21,22)(20,23,24)(25,27,26)(28,34,31)(29,33,30)(32,35,36)(37,40,41)(38,39,42), (25,28,29)(26,30,31)(27,33,34)(36,41,42), (25,29,28)(26,30,31)(27,34,33)(32,37,38), (25,28,29)(27,34,33)(32,38,37)(36,42,41), (25,29,28)(26,31,30)(32,38,37)(36,41,42), (25,29,28)(26,30,31)(27,33,34)(32,38,37)(35,39,40)(36,42,41));