C₅×#63553 #13084778

order	1440
isoclinism	isoclinic class of D₃²
automorphism	?
homology	Abelianization (H₁) = C₄×C₅×C₈ · Schur multiplier (H₂) = C₄

Aliases

derived, Sylow	C₃² ⋊ C₄×C₅×C₈
Hall	C₃²×C₅ ⋊ C₄×C₈

206 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 2 generators on 23 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 1095);