C₂×C₆₇×#1780 #30699829

order	17152
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₆₇ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂×C₆₇×#1780

Subgroups

	subgroup	G/H
center	C₂³×C₄×C₆₇	C₂³
commutator	C₂³	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
socle	C₂⁴×C₆₇	C₂²×C₄
prime radical	C₂³×#41×C₆₇	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₆₇ ◁ 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) = 93
transitive degree	μ_t(G) = 8576

A minimal faithful permutation representation — 4 generators on 93 points:

(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(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

5896 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 13566);