C₁₇×#1459 #14524465

order	2176
nilpotency class	3
isoclinism	isoclinic class of #99
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#1459

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂²⋊C₄
commutator	C₂²	C₂²×C₈×C₁₇
Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
socle	C₂²×C₁₇	C₂×C₂²⋊C₄
prime radical	C₂²×D₄×C₁₇	C₄
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

332 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 124 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)(26,27,29,32,30,33,28,31);(18,20)(19,22)(21,25)(23,24);(26,28,30,29)(27,31,33,32)

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16921318, #16921324, #16921541, …
maximal subgroup of	C₁₇×#7203, C₁₇×#7205, C₁₇×#7285, …
maximal normal subgroup of	C₁₇×#7203, C₁₇×#7205, C₁₇×#7285, …
maximal quotient of	C₁₇×#7565, C₁₇×#7566, C₁₇×#7582, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 191);