C₄×C₇×C₂₃² #28414476

order	14812
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂₃

Aliases

abelian

C₄×C₇×C₂₃²

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₇×C₂₃²
socle, prime radical	C₂×C₇×C₂₃²	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 14812

A minimal faithful permutation representation — 2 generators on 57 points:

(1,2,3,4)(5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34);(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57)

Conjugacy classes & character table

14812 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×C₈×C₂₃², C₂×C₄×C₇×C₂₃²
maximal normal subgroup of	C₇×C₈×C₂₃², C₂×C₄×C₇×C₂₃²
maximal quotient of	C₇×C₈×C₂₃², C₂×C₄×C₇×C₂₃²

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14812, 10);

C4×C7×C232 #28414476