C₂³×C₇×#124 #13239876

order	1792
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₇ · Schur multiplier (H₂) = C₂¹³×C₄

Aliases

C₂³×C₇×#124

	subgroup	G/H
center, socle	C₂⁵×C₇	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
prime radical	C₂⁴×C₇×D₄	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁵×C₇ ◁ G

14334 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 896

A minimal faithful permutation representation — 6 generators on 25 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 55648);