C₂×C₉×C₅⋊D₁₄₅ #39907986

order	26100
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₂×C₉×C₅⋊D₁₄₅
unambiguous semidirect product	(C₂×C₅)⋊(C₉×D₁₄₅)
unambiguous semidirect product	(C₂×C₂₉)⋊(C₉×C₅⋊D₅)

Splittings

Fitting	C₂×C₅²×C₉×C₂₉ ⋊ C₂
derived, Hall	C₅²×C₂₉ ⋊ C₂²×C₉
Hall	C₅²×C₉×C₂₉ ⋊ C₂²
Hall	C₉×C₂₉ ⋊ C₂×C₅⋊D₅
Hall	C₅²×C₉ ⋊ C₂×D₂₉
Sylow	C₂₉ ⋊ C₂×C₉×C₅⋊D₅
Sylow	C₅² ⋊ C₂×C₉×D₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉	C₅⋊D₁₄₅
commutator, hypocenter	C₅²×C₂₉	C₂²×C₉
Frattini	C₃	C₂×C₃×C₅⋊D₁₄₅
Fitting	C₂×C₅²×C₉×C₂₉	C₂
socle	C₂×C₃×C₅²×C₂₉	C₂×C₃
prime radical	C₂×C₃×C₅⋊D₁₄₅	C₃
cosocle	C₃×C₅²×C₂₉	C₂²×C₃
LCS	G ▷ C₅²×C₂₉
UCS	C₁ ◁ C₂×C₉

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 50
transitive degree	μ_t(G) = 13050

A minimal faithful permutation representation — 3 generators on 50 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)(30,34,38,32,37,33,35,31,36)(40,41)(42,43)(45,46)(47,48);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(44,45,47,48,46)(49,50);(39,40,42,43,41)

Conjugacy classes & character table

6552 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26100, 220);

C2×C9×C5⋊D145 #39907986