C₁₇×#2860 #14525866

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#2860

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₇
prime radical	C₂²×D₄×C₁₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

516 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 216 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 — 4 generators on 37 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(23,24)(27,28)(32,35)(33,37);(22,23,26,24)(25,27,29,28)(30,31,34,36)(32,33,35,37);(18,19,20,21)(22,24,26,23)(25,28,29,27)(30,32,34,35)(31,33,36,37);(22,25,26,29)(23,27,24,28)(30,33)(31,35)(32,36)(34,37)

Conjugacy classes & character table

748 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16922710, #16922738, #16922802, …
maximal subgroup of	C₁₇×#7666, C₁₇×#7672, C₁₇×#7686, …
maximal normal subgroup of	C₁₇×#7666, C₁₇×#7672, C₁₇×#7686, …
maximal quotient of	C₁₇×#14688, C₁₇×#14699, C₁₇×#14700, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1592);