C₂×C₇×#2030 #13200682

order	1792
nilpotency class	3
isoclinism	isoclinic class of #2021
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂×C₇×#2030

Subgroups

	subgroup	G/H
center, socle	C₂³×C₇	#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₇
prime radical	C₂⁵×C₇	C₂³
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂⁵×C₇ ◁ G

1482 conjugacy classes of subgroups; only the 350 normal subgroups are shown.

normal subgroups only

This group has 1482 conjugacy classes of subgroups — too many to draw. Only its 350 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) = 448

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

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

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, 16454);