C₁₇×#1817 #14524823

order	2176
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#1817

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₇	C₂³
commutator	C₂²	C₂²×C₈×C₁₇
Frattini, cosocle	C₂²×C₄	C₂³×C₁₇
socle	C₂³×C₁₇	C₂²×C₄
prime radical	C₂⁴×C₁₇	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₇ ◁ G

380 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 160 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)(18,19)(20,21)(22,23)(24,27)(25,26)(28,29)(30,31,32,34,33,35,36,37);(23,26)(27,29);(19,21)(22,24,25,28)(23,27,26,29)

Conjugacy classes & character table

952 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16920855, #16920863, #16920896, …
maximal subgroup of	C₁₇×#7017, C₁₇×#7021, C₁₇×#7033, …
maximal normal subgroup of	C₁₇×#7017, C₁₇×#7021, C₁₇×#7033, …
maximal quotient of	C₁₇×#8698, C₁₇×#8699, C₁₇×#8700, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 549);