D₁₇×#11725077 #44472528

order	29988
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

D₁₇×#11725077

Splittings

derived, Hall	C₇²×C₁₇ ⋊ C₂²×C₉
Hall	C₁₇×#89204 ⋊ C₂²
Hall	D₁₇×C₇⋊D₇ ⋊ C₉
Hall	#89204 ⋊ C₂×D₁₇
Sylow	C₇² ⋊ C₂×C₉×D₁₇
Sylow	C₁₇ ⋊ C₂×#11725077

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₃	D₁₇×#64424
commutator, hypocenter	C₇²×C₁₇	C₂²×C₉
Fitting, socle, cosocle	C₃×C₇²×C₁₇	C₂²×C₃
prime radical	C₃×D₁₇×C₇⋊D₇	C₃
LCS	G ▷ C₇²×C₁₇
UCS	C₁ ◁ C₃

300 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 7497

A minimal faithful permutation representation — 3 generators on 40 points:

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

Conjugacy classes & character table

420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29988, 169);

D17×#11725077 #44472528