C₁₇×D₁₁₅ #16840936

order	3910
isoclinism	isoclinic class of D₁₁₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×D₁₁₅
unambiguous semidirect product	C₅⋊(C₁₇×D₂₃)
unambiguous semidirect product	C₂₃⋊(D₅×C₁₇)

Splittings

Fitting, socle, Hall	C₅×C₁₇×C₂₃ ⋊ C₂
derived, Hall	C₅×C₂₃ ⋊ C₂×C₁₇
Hall	C₁₇×C₂₃ ⋊ D₅
Hall	C₅×C₁₇ ⋊ D₂₃
Sylow	C₂₃ ⋊ D₅×C₁₇
Sylow	C₅ ⋊ C₁₇×D₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₇	D₁₁₅
commutator, cosocle, hypocenter	C₅×C₂₃	C₂×C₁₇
Frattini	C₁	G
Fitting, socle	C₅×C₁₇×C₂₃	C₂
LCS	G ▷ C₅×C₂₃
UCS	C₁ ◁ C₁₇

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 1955

A minimal faithful permutation representation — 2 generators on 45 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);(19,22)(20,21)(24,45)(25,44)(26,43)(27,42)(28,41)(29,40)(30,39)(31,38)(32,37)(33,36)(34,35)

Conjugacy classes & character table

1003 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₁₇×D₁₁₅, C₁₇×D₃₄₅, C₁₇×D₅₇₅, …
maximal normal subgroup of	C₃×C₁₇×D₁₁₅, C₅×C₁₇×D₁₁₅, C₇×C₁₇×D₁₁₅
maximal quotient of	C₃×C₁₇×D₁₁₅, C₁₇×D₃₄₅, C₁₇×D₅₇₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3910, 6);

C17×D115 #16840936