C₁₇×#1347 #14524353

order	2176
nilpotency class	4
isoclinism	isoclinic class of #1347
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#1347

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#102
commutator	C₂×C₈	C₂×C₄×C₁₇
Frattini, cosocle	C₂²×C₈	C₂²×C₁₇
prime radical	C₁₇×#466	C₂
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂²×C₈×C₁₇ ◁ G

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

normal subgroups only

This group has 126 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) = 544

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)(20,24,25,22)(21,23)(26,27)(28,31)(29,38)(30,34)(32,35)(33,36)(37,40)(39,41);(18,20)(19,22)(21,25)(23,24)(27,31)(28,35)(29,36)(32,33)(34,40)(37,41)(38,39)

Conjugacy classes & character table

493 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₇×#1347, #16944549, #16944554, …
maximal subgroup of	C₂×C₁₇×#1347, C₁₇×#11703, C₁₇×#11704, …
maximal normal subgroup of	C₂×C₁₇×#1347, C₁₇×#11703, C₁₇×#11704, …
maximal quotient of	C₁₇×#7076, C₁₇×#7079, C₁₇×#7088, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 79);