C₅×#67602 #14279256

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅×#67602

Splittings

Fitting	C₃×C₅×M₆₄ ⋊ C₂
Hall	C₃×C₅ ⋊ #1400
Sylow	C₃ ⋊ C₅×#1400

Subgroups

	subgroup	G/H
center	C₅×C₈	(C₂×D₃)⋊C₄
commutator	C₂²×C₃	C₂×C₅×C₁₆
Frattini	C₂×C₁₆	C₂×C₅×D₃
Fitting	C₃×C₅×M₆₄	C₂
socle	C₂×C₃×C₅	C₂²⋊C₁₆
prime radical	C₂²×C₅×D₃	C₁₆
cosocle	C₂×C₃×C₁₆	C₂²×C₅
hypercenter	C₅×M₆₄	D₃
hypocenter	C₃	C₅×#1400
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₅×C₈ ◁ C₂×C₅×C₁₆ ◁ C₅×M₆₄

148 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

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

Full subgroup data →

Presentation

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 2 generators on 40 points:

(1,2,3,4,5)(7,8)(10,15)(11,19)(17,26)(18,27)(20,31)(21,32)(30,37)(33,39);(6,7,8)(9,10,11,16,12,17,20,28,13,18,21,29,22,30,33,38,14,15,19,25,23,26,31,35,24,27,32,36,34,37,39,40)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 4954);