SL(2,ℤ/4)×AGL(1,𝔽₁₃) #72242279

order	7488
automorphism	?
homology	Abelianization (H₁) = C₃×C₄² · Schur multiplier (H₂) = C₂×C₄

Aliases

derived	A₄×C₁₃ ⋊ C₃×C₄²
Sylow	C₁₃ ⋊ C₃×C₄×SL(2,ℤ/4)

	subgroup	G/H
center, Frattini, hypercenter	C₂	S₄×AGL(1,𝔽₁₃)
commutator, hypocenter	A₄×C₁₃	C₃×C₄²
Fitting, socle	C₂³×C₁₃	C₃×C₄×D₃
prime radical	C₂×A₄×D₁₃⋊C₃	C₂²
cosocle	C₂×A₄×D₁₃	C₂²×C₃
LCS	G ▷ A₄×C₁₃
UCS	C₁ ◁ C₂

532 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 69 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) = 156

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

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

maximal subgroup of	GL(2,ℤ/4)×AGL(1,𝔽₁₃)
maximal normal subgroup of	GL(2,ℤ/4)×AGL(1,𝔽₁₃)

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

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