#535×C₇₃ #17988254

order	4672
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₃ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

#535×C₇₃

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₇₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ G

334 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 162 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) = 85
transitive degree	μ_t(G) = 1168

A minimal faithful permutation representation — 4 generators on 85 points:

(2,4)(6,9)(7,11)(13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85);(5,6,8,9)(7,10,11,12);(1,2)(3,4)(5,6)(7,10)(8,9)(11,12);(5,7)(6,10)(8,11)(9,12)

Conjugacy classes & character table

1606 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#34004156, #34004507, #34004520, …
maximal subgroup of	C₇₃×#1910, C₇₃×#1911, C₇₃×#1914, …
maximal normal subgroup of	C₇₃×#1910, C₇₃×#1911, C₇₃×#1914, …
maximal quotient of	C₇₃×#2309, C₇₃×#2311, C₇₃×#2317, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4672, 216);