C₂₉×#539 #14270834

order	1856
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₉×#539

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₂₉
prime radical	C₂₉×#121	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ G

218 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 146 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) = 45
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 4 generators on 45 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)(30,31)(32,33)(34,35)(36,37)(40,44)(42,45);(31,35)(32,36)(38,39,41,43)(40,42,44,45);(30,32,34,36)(31,33,35,37)(38,40)(39,42)(41,44)(43,45);(30,33)(31,36)(32,35)(34,37)

Conjugacy classes & character table

638 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16818421, #16818455, #16818489, …
maximal subgroup of	C₂₉×#1597, C₂₉×#1603, C₂₉×#1609, …
maximal normal subgroup of	C₂₉×#1597, C₂₉×#1603, C₂₉×#1609, …
maximal quotient of	C₂₉×#2313, C₂₉×#2318, C₂₉×#2322, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1856, 220);