C₅×GL(2,𝔽₃)⋊C₈ #14510743

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₈ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×GL(2,𝔽₃)⋊C₈
unambiguous semidirect product	GL(2,𝔽₃)⋊(C₅×C₈)

Fitting	C₅×C₈×Q₈ ⋊ D₃
derived	SL(2,𝔽₃) ⋊ C₂×C₅×C₈

224 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.

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

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 320

A minimal faithful permutation representation — 2 generators on 29 points:

(1,2,3,4,5)(6,7,8,10,9,11,12,13)(14,24,26)(15,20,29,19,25,28)(16,23,18)(21,22);(14,15)(16,22)(17,25)(18,19)(20,27)(21,24)(23,29)(26,28)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236441);