C₄×C₇²×C₇₉ #29509228

order	15484
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₇

Aliases

abelian

C₄×C₇²×C₇₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₇²×C₇₉
socle, prime radical	C₂×C₇²×C₇₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 97
transitive degree	μ_t(G) = 15484

A minimal faithful permutation representation — 2 generators on 97 points:

(1,2,3,4)(5,6,7,8,9,10,11)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97);(12,13,14,15,16,17,18)

Conjugacy classes & character table

15484 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇²×C₈×C₇₉, C₂×C₄×C₇²×C₇₉
maximal normal subgroup of	C₇²×C₈×C₇₉, C₂×C₄×C₇²×C₇₉
maximal quotient of	C₇²×C₈×C₇₉, C₂×C₄×C₇²×C₇₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15484, 10);

C4×C72×C79 #29509228