C₁₇×#2633 #14525639

order	2176
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₇×#2633

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

512 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 192 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)(23,26)(27,29)(30,31,34,32)(33,35,37,36);(19,21)(23,26)(27,29)(31,32)(35,36);(18,19)(20,21)(22,23)(24,27)(25,26)(28,29)(30,32,34,31)(33,35,37,36);(22,24,25,28)(23,27,26,29)(30,33)(31,35)(32,36)(34,37)

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#16930318, #16935207, #16935235, …
maximal subgroup of	C₁₇×#9189, C₁₇×#10019, C₁₇×#10023, …
maximal normal subgroup of	C₁₇×#9189, C₁₇×#10019, C₁₇×#10023, …
maximal quotient of	C₁₇×#14269, C₁₇×#14289, C₁₇×#14298, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 1365);