C₁₇×#2659 #14525665

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#2659

Subgroups

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

524 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 232 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) = 37
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 4 generators on 37 points:

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

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16934878, #16934883, #16934912, …
maximal subgroup of	C₁₇×#9966, C₁₇×#9967, C₁₇×#9972, …
maximal normal subgroup of	C₁₇×#9966, C₁₇×#9967, C₁₇×#9972, …
maximal quotient of	C₁₇×#14275, C₁₇×#14281, C₁₇×#14327, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1391);