C₁₇×#1519 #14524525

order	2176
nilpotency class	3
isoclinism	isoclinic class of #1504
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#1519

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	C₂×C₁₇×#121	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

340 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 108 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)(18,19)(20,24,25,22)(21,23)(26,27)(28,32)(29,31)(30,33);(18,20)(19,22)(21,25)(23,24)(27,31)(28,29)(32,33);(20,25)(22,24)(26,28,30,29)(27,31,33,32)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16925853, #16925863, #16925984, …
maximal subgroup of	C₁₇×#8350, C₁₇×#8352, C₁₇×#8375, …
maximal normal subgroup of	C₁₇×#8350, C₁₇×#8352, C₁₇×#8375, …
maximal quotient of	C₁₇×#7572, C₁₇×#7573, C₁₇×#7586, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 251);