C₅×C₂²⋊(#95⋊C₃) #14511007

order	1920
automorphism	?
homology	Abelianization (H₁) = C₃×C₅ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product	C₅×C₂²⋊(#95⋊C₃)
unambiguous semidirect product	C₂²⋊(C₅×#95⋊C₃)
unambiguous semidirect product	(C₂²×C₅)⋊(#95⋊C₃)

Fitting, Hall	C₂²×C₅×#95 ⋊ C₃
derived, Sylow	C₂²×#95 ⋊ C₃×C₅

	subgroup	G/H
center, hypercenter	C₂×C₅	C₂²⋊(C₄²⋊C₃)
commutator, cosocle, hypocenter	C₂²×#95	C₃×C₅
Frattini	C₂³	C₅×C₂²⋊A₄
Fitting	C₂²×C₅×#95	C₃
socle	C₂⁵×C₅	A₄
LCS	G ▷ C₂²×#95
UCS	C₁ ◁ C₂×C₅

690 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.

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

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 120

A minimal faithful permutation representation — 3 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236705);