C₆₇×#7395 #30686646

order	17152
nilpotency class	5
isoclinism	isoclinic class of #7394
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₆₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₆₇×#7395

Subgroups

	subgroup	G/H
center, socle	C₂×C₆₇	#1343
commutator	C₂×C₂²⋊C₄	C₂×C₄×C₆₇
Frattini, cosocle	#381	C₂²×C₆₇
prime radical	#534×C₆₇	C₄
LCS	G ▷ C₂×C₂²⋊C₄ ▷ C₂⁴ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₆₇ ◁ C₂³×C₆₇ ◁ C₂⁴×C₆₇ ◁ #381×C₆₇ ◁ G

284 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 42 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 — 2 generators on 99 points:

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

Conjugacy classes & character table

1675 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 383);