#45692068

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

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, Hall	C₇²×C₁₉ ⋊ C₂²×C₉
Hall	#22552719 ⋊ C₂²
Hall	D₁₉×C₇⋊D₇ ⋊ C₉
Sylow	C₇² ⋊ C₂×AGL(1,𝔽₁₉)
Sylow	C₁₉ ⋊ C₂×#11725077

Subgroups

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

300 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 931

A minimal faithful permutation representation — 3 generators on 33 points:

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

Polycyclic presentation:

2^2,3^2,7^2,19|c^3=d,g^a=g^18,e^b=e^6,f^b=f^6,e^c=e^2,f^c=f^2,g^c=g^16,g^d=g^11

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 866);