C₂×C₇×#1663 #13196205

order	1792
nilpotency class	3
isoclinism	isoclinic class of #1655
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×C₇×#1663

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₇	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₄²×C₇ ◁ G

830 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 238 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) = 41
transitive degree	μ_t(G) = 1792

A minimal faithful permutation representation — 4 generators on 41 points:

(1,2)(35,36,37,38,39,40,41);(3,4,9,13)(5,14,16,17)(6,15,10,18)(7,12,8,11)(19,20,24,22)(21,27,30,34)(23,31,33,26)(25,32,28,29);(3,5)(4,10)(6,13)(7,18)(8,15)(9,16)(11,17)(12,14)(19,21,24,30)(20,25,22,28)(23,32,33,29)(26,34,31,27);(3,6,9,10)(4,5,13,16)(7,17,8,14)(11,15,12,18)(19,22,24,20)(21,28,30,25)(23,26,33,31)(27,32,34,29)

Conjugacy classes & character table

280 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 11977);