C₄²×#11719908 #27298911

order	13568
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₆ · Schur multiplier (H₂) = C₄³

Aliases

direct product

C₄²×#11719908

Splittings

derived, Sylow

C₅₃ ⋊ C₄²×C₁₆

Subgroups

	subgroup	G/H
center, hypercenter	C₄²×C₈	D₅₃
commutator, hypocenter	C₅₃	C₄²×C₁₆
Frattini	C₂²×C₈	C₂²×D₅₃
Fitting	C₄²×C₈×C₅₃	C₂
socle, prime radical	C₂³×C₅₃	C₂²×C₈
cosocle	C₂²×C₈×C₅₃	C₂³
LCS	G ▷ C₅₃
UCS	C₁ ◁ C₄²×C₈

558 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 77
transitive degree	μ_t(G) = 13568

A minimal faithful permutation representation — 3 generators on 77 points:

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

Conjugacy classes & character table

3584 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 84387);

C42×#11719908 #27298911