C₁₇×#1509 #14524515

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1504
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#1509

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×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

242 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 92 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) = 544

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)(19,22)(20,24)(23,25)(27,31,32,33);(18,19)(20,25)(21,23)(22,24)(26,27)(28,31)(29,33)(30,32);(19,23)(22,25)(26,28,30,29)(27,31,32,33)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16926207, #16926214, #16926221, …
maximal subgroup of	C₁₇×#8416, C₁₇×#8417, C₁₇×#8418, …
maximal normal subgroup of	C₁₇×#8416, C₁₇×#8417, C₁₇×#8418, …
maximal quotient of	C₁₇×#7574, C₁₇×#7577, C₁₇×#7584, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 241);