C₁₃×#64418 #16838486

order	3822
isoclinism	isoclinic class of #64418
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center, hypercenter	C₁₃	#64418
commutator, cosocle, hypocenter	#3862	C₂×C₁₃
Frattini	C₁	G
Fitting, socle	C₇²×C₁₃	D₃
LCS	G ▷ #3862
UCS	C₁ ◁ C₁₃

28 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 182

A minimal faithful permutation representation — 2 generators on 27 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3822, 79);