C₂×C₇×#2845 #13213905

order	1792
nilpotency class	2
isoclinism	isoclinic class of #2812
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₇ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₂×C₇×#2845

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇ ◁ G

1742 conjugacy classes of subgroups; only the 974 normal subgroups are shown.

normal subgroups only

This group has 1742 conjugacy classes of subgroups — too many to draw. Only its 974 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 — 5 generators on 33 points:

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

Conjugacy classes & character table

364 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 29677);