D₃₅×D₉₅ #27210917

order	13300
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

direct product

D₃₅×D₉₅

Splittings

Fitting, socle, derived, Hall	C₅²×C₇×C₁₉ ⋊ C₂²
Hall	C₅²×C₁₉ ⋊ C₂×D₇
Hall	C₅²×C₇ ⋊ C₂×D₁₉
Hall	C₇×C₁₉ ⋊ D₅²
Sylow	C₅² ⋊ D₇×D₁₉
Sylow	C₁₉ ⋊ D₅×D₃₅
Sylow	C₇ ⋊ D₅×D₉₅

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₇×C₁₉	C₂²
LCS	G ▷ C₅²×C₇×C₁₉
UCS	C₁

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 36
transitive degree	μ_t(G) = 1330

A minimal faithful permutation representation — 2 generators on 36 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21,23,25,26,24,22)(27,28,30,31,29)(33,34)(35,36);(1,2,4,6,8,10,12,14,16,18,19,17,15,13,11,9,7,5,3)(21,22)(23,24)(25,26)(28,29)(30,31)(32,33,35,36,34)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13300, 75);

D35×D95 #27210917