#14558781⋊D₇ #45691583

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

Aliases

unambiguous semidirect product

#14558781⋊D₇

Splittings

derived, Hall	C₇²×C₁₉ ⋊ C₂²×C₉
Hall	C₇×#11924777 ⋊ C₂²
Hall	D₁₉×C₇⋊D₇ ⋊ C₉
Sylow	C₇² ⋊ C₂×#4294⋊C₂
Sylow	C₁₉ ⋊ C₂×(C₇⋊C₉)⋊D₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₃	#11716322⋊D₇
commutator, hypocenter	C₇²×C₁₉	C₂²×C₉
Fitting, socle, cosocle	C₃×C₇²×C₁₉	C₂²×C₃
prime radical	C₃×D₁₉×C₇⋊D₇	C₃
LCS	G ▷ C₇²×C₁₉
UCS	C₁ ◁ C₃

160 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 39 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) = 42
transitive degree	μ_t(G) = 1197

A minimal faithful permutation representation — 2 generators on 42 points:

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

Polycyclic presentation:

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

Conjugacy classes & character table

366 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 381);