C₂₉×#548 #14270843

order	1856
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₉×#548

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₂₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ G

290 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 166 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) = 41
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 4 generators on 41 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)(31,33)(35,38)(39,40);(34,35,37,38)(36,40,41,39);(30,31)(32,33);(34,36,37,41)(35,39,38,40)

Conjugacy classes & character table

725 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16830988, #16831048, #16831058, …
maximal subgroup of	C₂₉×#3265, C₂₉×#3269, C₂₉×#3270, …
maximal normal subgroup of	C₂₉×#3265, C₂₉×#3269, C₂₉×#3270, …
maximal quotient of	Q₈×C₂²⋊C₄×C₂₉, C₂₉×#2341, C₂₉×#2351, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1856, 229);