C₁₇×#535 #11762476

order	1088
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₁₇×#535

Subgroups

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

334 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 162 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) = 29
transitive degree	μ_t(G) = 272

A minimal faithful permutation representation — 4 generators on 29 points:

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

Conjugacy classes & character table

374 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#14529312, #14529317, #14529332, …
maximal subgroup of	C₁₇×#1910, C₁₇×#1911, C₁₇×#1914, …
maximal normal subgroup of	C₁₇×#1910, C₁₇×#1911, C₁₇×#1914, …
maximal quotient of	C₁₇×#2309, C₁₇×#2311, C₁₇×#2317, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1088, 216);