C₂⁴×C₁₉⋊C₃ #11745003

order	912
isoclinism	isoclinic class of C₁₉⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂⁴×C₁₉⋊C₃

Fitting, socle, Hall	C₂⁴×C₁₉ ⋊ C₃
derived, Sylow	C₁₉ ⋊ C₂⁴×C₃

	subgroup	G/H
center, hypercenter	C₂⁴	C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₂⁴×C₃
Frattini	C₁	G
Fitting, socle	C₂⁴×C₁₉	C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂⁴

268 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 304

A minimal faithful permutation representation — 4 generators on 27 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(912, 214);