#45692095

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

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, Hall	C₇²×C₁₉ ⋊ C₂²×C₉
Hall	#22552721 ⋊ C₂²
Hall	D₁₉×C₇⋊D₇ ⋊ C₉
Sylow	C₇² ⋊ C₂×AGL(1,𝔽₁₉)
Sylow	C₁₉ ⋊ C₂×#11725078

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

160 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 32 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) = 33
transitive degree	μ_t(G) = 399

A minimal faithful permutation representation — 2 generators on 33 points:

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

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^4,g^c=g^4,g^d=g^7

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, 893);