S₄×C₄⋊AGL(1,𝔽₇) #72244688

order	4032
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂⁴

Aliases

Fitting	C₂²×C₄×C₇ ⋊ C₂×C₃×D₃
Sylow	C₇ ⋊ C₃×D₄×S₄

968 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 968 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.

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

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 84

A minimal faithful permutation representation — 3 generators on 15 points:

(1,2,3,4)(5,7,8,6)(9,10,15)(11,12,14);(2,4)(10,11)(12,14)(13,15);(7,8)

maximal subgroup of	D₄×S₄×AGL(1,𝔽₇)
maximal normal subgroup of	D₄×S₄×AGL(1,𝔽₇)

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

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