C₂⁴×C₃×#1094 #72244761

order	5184
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃³ · Schur multiplier (H₂) = C₂⁷×C₃²

Aliases

C₂⁴×C₃×#1094

C₂⁶ ⋊ C₃×3₋¹⁺²

30208 conjugacy classes of subgroups; only the 2814 normal subgroups are shown.

normal subgroups only

This group has 30208 conjugacy classes of subgroups — too many to draw. Only its 2814 normal subgroups are shown.

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

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 432

A minimal faithful permutation representation — 4 generators on 24 points:

(7,8)(9,10,11)(12,15)(13,14);(5,6)(13,15,14)(16,19,24,18,22,20,21,17,23);(3,4)(17,19,22)(20,24,23);(1,2)

960 conjugacy classes. The character table is too large to display.

maximal subgroup of	C₂²×#72220143, C₂²×#72220152
maximal normal subgroup of	C₂²×#72220143, C₂²×#72220152

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

gap> G := Group((7,8)(9,10,11)(12,15)(13,14), (5,6)(13,15,14)(16,19,24,18,22,20,21,17,23), (3,4)(17,19,22)(20,24,23), (1,2));