C₁₇×#2817 #14525823

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2812
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#2817

Subgroups

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

444 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 184 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) = 45
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 4 generators on 45 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(23,26)(27,29)(30,31,35,33)(32,38,40,36)(34,37,43,41)(39,45,42,44);(19,21)(23,26)(24,28)(30,32,35,40)(31,36,33,38)(34,42,43,39)(37,45,41,44);(18,19)(20,21)(22,23)(24,27)(25,26)(28,29)(30,33,35,31)(32,36,40,38)(34,37,43,41)(39,45,42,44);(22,24)(23,27)(25,28)(26,29)(30,34,35,43)(31,37,33,41)(32,39,40,42)(36,44,38,45)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16934968, #16934985, #16946382, …
maximal subgroup of	C₁₇×#9982, C₁₇×#9985, C₁₇×#12095, …
maximal normal subgroup of	C₁₇×#9982, C₁₇×#9985, C₁₇×#12095, …
maximal quotient of	C₁₇×#14626, C₁₇×#14627, C₁₇×#14629, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1549);