C₁₇×#1360 #14524366

order	2176
nilpotency class	4
isoclinism	isoclinic class of #1347
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#1360

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#102
commutator	C₂×C₈	C₂×C₄×C₁₇
Frattini, cosocle	C₄×C₈	C₂²×C₁₇
prime radical	C₂×D₈×C₁₇	C₄
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₄×C₈×C₁₇ ◁ G

102 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 102 conjugacy classes of subgroups — too many to draw. Only its 44 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) = 41
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 2 generators on 41 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,23,21,22,24,25)(27,32,33,40)(28,36)(29,30)(34,37,35,41)(38,39);(19,22)(20,24)(26,27)(28,37)(29,35)(30,34)(31,33)(32,38)(36,40)(39,41)

Conjugacy classes & character table

493 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1360, #16945546, #16945550, …
maximal subgroup of	C₂×C₁₇×#1360, C₁₇×#11924, C₁₇×#11925, …
maximal normal subgroup of	C₂×C₁₇×#1360, C₁₇×#11924, C₁₇×#11925, …
maximal quotient of	C₁₇×#7092, C₁₇×#7093, C₁₇×#7094, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 92);