C₂×D₃²×#97 #72228222

order	2304
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂¹⁰

Aliases

C₂×D₃²×#97

Fitting	C₂×C₃²×#97 ⋊ C₂²
Sylow	C₃² ⋊ C₂³×#97

8592 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 384

A minimal faithful permutation representation — 5 generators on 20 points:

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

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

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

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