C₆₇×#13429 #30692680

order	17152
nilpotency class	4
isoclinism	isoclinic class of #13429
automorphism	?
homology	Abelianization (H₁) = C₂³×C₆₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₆₇×#13429

Subgroups

	subgroup	G/H
center, socle	C₂×C₆₇	#2044
commutator, Frattini, cosocle	C₂×#41	C₂³×C₆₇
prime radical	C₆₇×#3199	C₂
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₆₇ ◁ C₂×C₄×C₆₇ ◁ C₂×#41×C₆₇ ◁ G

434 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 86 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) = 99
transitive degree	μ_t(G) = 2144

A minimal faithful permutation representation — 3 generators on 99 points:

(1,2)(3,12)(4,7)(5,10)(6,11)(8,15)(9,16)(13,25)(14,29)(17,21)(18,23)(19,26)(20,30)(22,32)(24,31)(27,28)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(2,7)(3,13)(4,16)(8,20)(9,11)(10,21)(12,27)(17,31)(22,23)(24,26)(25,29)(30,32);(1,3,4,14,6,13,16,28)(2,8,9,22,11,23,7,20)(5,18,17,32,19,15,31,30)(10,25,24,29,26,12,21,27)

Conjugacy classes & character table

1876 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 6417);