C₁₇×#2207 #14525213

order	2176
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#2207

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₇
prime radical	C₁₇×#493	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₄×C₈×C₁₇ ◁ G

174 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 68 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 — 3 generators on 37 points:

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

Conjugacy classes & character table

493 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16947754, #16947761, #16947810, …
maximal subgroup of	C₁₇×#12317, C₁₇×#12318, C₁₇×#12325, …
maximal normal subgroup of	C₁₇×#12317, C₁₇×#12318, C₁₇×#12325, …
maximal quotient of	C₁₇×#12417, C₁₇×#12425, C₁₇×#12446, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 939);