C₁₆×#11719908 #27270705

order	13568
automorphism	?
homology	Abelianization (H₁) = C₁₆² · Schur multiplier (H₂) = C₁₆

Aliases

direct product

C₁₆×#11719908

Splittings

derived, Sylow

C₅₃ ⋊ C₁₆²

Subgroups

	subgroup	G/H
center, hypercenter	C₈×C₁₆	D₅₃
commutator, hypocenter	C₅₃	C₁₆²
Frattini	C₈²	C₂×D₅₃
Fitting	C₈×C₁₆×C₅₃	C₂
socle, prime radical	C₂²×C₅₃	C₈²
cosocle	C₈²×C₅₃	C₂²
LCS	G ▷ C₅₃
UCS	C₁ ◁ C₈×C₁₆

166 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 85
transitive degree	μ_t(G) = 13568

A minimal faithful permutation representation — 2 generators on 85 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)(70,71,72,75,73,76,78,81,74,77,79,82,80,83,84,85);(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)(54,55,56,59,57,60,62,65,58,61,63,66,64,67,68,69)

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, 56181);

C16×#11719908 #27270705