(C₃₁⋊C₃)⋊Dic₇ #14579593

order	2604
isoclinism	isoclinic class of (C₃₁⋊C₃)⋊D₇
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

(C₃₁⋊C₃)⋊Dic₇

	subgroup	G/H
center, Frattini, hypercenter	C₂	(C₃₁⋊C₃)⋊D₇
commutator, hypocenter	C₇×C₃₁	C₃×C₄
Fitting, socle, cosocle	C₂×C₇×C₃₁	C₂×C₃
prime radical	C₂×C₇×C₃₁⋊C₃	C₂
LCS	G ▷ C₇×C₃₁
UCS	C₁ ◁ C₂

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 42
transitive degree	μ_t(G) = 868

Polycyclic presentation:

2,3,7,31,2|a^2=e,c^a=c^6,d^a=d^30,d^b=d^5

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2604, 4);