C₁₃×D₁₇₇ #17987177

order	4602
isoclinism	isoclinic class of D₁₇₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×D₁₇₇
unambiguous semidirect product	C₃⋊(C₁₃×D₅₉)
unambiguous semidirect product	C₅₉⋊(D₃×C₁₃)

Splittings

Fitting, socle, Hall	C₃×C₁₃×C₅₉ ⋊ C₂
derived, Hall	C₃×C₅₉ ⋊ C₂×C₁₃
Hall	C₁₃×C₅₉ ⋊ D₃
Sylow	C₅₉ ⋊ D₃×C₁₃
Hall	C₃×C₁₃ ⋊ D₅₉
Sylow	C₃ ⋊ C₁₃×D₅₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃	D₁₇₇
commutator, cosocle, hypocenter	C₃×C₅₉	C₂×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₅₉	C₂
LCS	G ▷ C₃×C₅₉
UCS	C₁ ◁ C₁₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 75
transitive degree	μ_t(G) = 2301

A minimal faithful permutation representation — 2 generators on 75 points:

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

Conjugacy classes & character table

1170 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₃×D₅₃₁, C₁₃⋊C₃×D₁₇₇, C₁₃×C₃⋊D₁₇₇, …
maximal normal subgroup of	C₁₃⋊C₃×D₁₇₇, C₃×C₁₃×D₁₇₇, C₅×C₁₃×D₁₇₇, …
maximal quotient of	C₁₃×D₅₃₁, C₁₃×C₃⋊D₁₇₇, C₃×C₁₃×D₁₇₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4602, 7);

C13×D177 #17987177