C₂×C₁₇×#1780 #16878322

order	4352
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂×C₁₇×#1780

Subgroups

	subgroup	G/H
center	C₂³×C₄×C₁₇	C₂³
commutator	C₂³	C₂³×C₄×C₁₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
socle	C₂⁴×C₁₇	C₂²×C₄
prime radical	C₂³×#41×C₁₇	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₇ ◁ G

4070 conjugacy classes of subgroups; only the 702 normal subgroups are shown.

normal subgroups only

This group has 4070 conjugacy classes of subgroups — too many to draw. Only its 702 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) = 43
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 4 generators on 43 points:

(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43);(3,4)(5,6)(7,8)(9,10)(11,12,14,17,15,18,21,24)(13,16,20,23,19,22,25,26);(4,6)(11,13)(12,16)(14,20)(15,19)(17,23)(18,22)(21,25)(24,26);(8,10)(13,19)(16,22)(20,25)(23,26)

Conjugacy classes & character table

1496 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 13566);