C₁₇×#62694 #16920438

order	4352
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₁₇ · Schur multiplier (H₂) = C₂¹³

Aliases

direct product

C₁₇×#62694

Subgroups

	subgroup	G/H
center	C₄²×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₇
socle	C₂²×C₁₇	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄²×C₁₇ ◁ G

6640 conjugacy classes of subgroups; only the 5670 normal subgroups are shown.

normal subgroups only

This group has 6640 conjugacy classes of subgroups — too many to draw. Only its 5670 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) = 49
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 6 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,26)(21,25)(22,24)(23,27)(28,32)(29,31)(30,33)(34,35)(36,39)(37,41)(38,40)(42,45)(43,46)(44,47)(48,49);(18,20)(19,23)(21,28)(22,27)(24,26)(25,30)(29,33)(31,32)(34,36)(35,39)(37,43)(38,42)(40,45)(41,46)(44,48)(47,49);(20,27)(23,26)(28,33)(30,32)(35,40)(36,42)(41,47)(43,48);(19,24)(23,26)(25,31)(30,32)(36,42)(39,45)(43,48)(46,49);(34,37,38,44)(35,41,40,47)(36,43,42,48)(39,46,45,49);(18,21,22,29)(19,25,24,31)(20,28,27,33)(23,30,26,32)

Conjugacy classes & character table

1292 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 55682);