C₁₇×#1504 #14524510

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1504
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#1504

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
prime radical	C₁₇×#525	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

334 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 96 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) = 33
transitive degree	μ_t(G) = 272

A minimal faithful permutation representation — 3 generators on 33 points:

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

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16925833, #16925838, #16926450, …
maximal subgroup of	C₁₇×#8346, C₁₇×#8347, C₁₇×#8453, …
maximal normal subgroup of	C₁₇×#8346, C₁₇×#8347, C₁₇×#8453, …
maximal quotient of	C₁₇×#7578, C₁₇×#7579, C₁₇×#7586, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 236);