C₂×C₇×#1713 #13196818

order	1792
nilpotency class	3
isoclinism	isoclinic class of #1705
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₂×C₇×#1713

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₇	#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₄²×C₇ ◁ G

878 conjugacy classes of subgroups; only the 382 normal subgroups are shown.

normal subgroups only

This group has 878 conjugacy classes of subgroups — too many to draw. Only its 382 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) = 33
transitive degree	μ_t(G) = 1792

A minimal faithful permutation representation — 4 generators on 33 points:

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

Conjugacy classes & character table

532 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 12590);