C₉×D₁₉×C₇⋊D₇ #45691662

order	33516
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂×C₇

Aliases

direct product

C₉×D₁₉×C₇⋊D₇

Splittings

Fitting, Hall	C₇²×C₉×C₁₉ ⋊ C₂²
derived, Hall	C₇²×C₁₉ ⋊ C₂²×C₉
Hall	C₇²×C₉ ⋊ C₂×D₁₉
Hall	C₉×C₁₉ ⋊ C₂×C₇⋊D₇
Sylow	C₇² ⋊ C₂×C₉×D₁₉
Sylow	C₁₉ ⋊ C₂×C₉×C₇⋊D₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₁₉×C₇⋊D₇
commutator, hypocenter	C₇²×C₁₉	C₂²×C₉
Frattini	C₃	C₃×D₁₉×C₇⋊D₇
Fitting	C₇²×C₉×C₁₉	C₂²
socle, cosocle	C₃×C₇²×C₁₉	C₂²×C₃
prime radical	C₃×D₁₉×C₇⋊D₇	C₃
LCS	G ▷ C₇²×C₁₉
UCS	C₁ ◁ C₉

300 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 42
transitive degree	μ_t(G) = 8379

A minimal faithful permutation representation — 3 generators on 42 points:

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

Conjugacy classes & character table

2574 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 460);

C9×D19×C7⋊D7 #45691662