AGL(1,𝔽₁₃)×#5935 #72259558

order	29952
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂³

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂	#1020×AGL(1,𝔽₁₃)
commutator, hypocenter	C₁₃×#997	C₂×C₃×C₄
Fitting	C₁₃×H(5,𝔽₂)	C₃×C₄×D₃
socle	C₂×C₁₃	C₃×C₄×#1020
prime radical	D₁₃⋊C₃×#5935	C₂
cosocle	D₁₃×#997	C₂²×C₃
LCS	G ▷ C₁₃×#997
UCS	C₁ ◁ C₂

2530 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 2530 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.

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

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 104

A minimal faithful permutation representation — 2 generators on 21 points:

(2,7,5)(3,8,6)(10,15,19,16,12,21,13,14,17,11,18,20);(1,5,7,2,4,8,3,6)(9,10,14,12,19,16,20,21,11,17,18,15,13)

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((2,7,5)(3,8,6)(10,15,19,16,12,21,13,14,17,11,18,20), (1,5,7,2,4,8,3,6)(9,10,14,12,19,16,20,21,11,17,18,15,13));