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C2×C32×C5⋊D145 #39908227

order26100
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3×C5

Aliases

direct productC2×C32×C5⋊D145
unambiguous semidirect product(C2×C5)⋊(C32×D145)
unambiguous semidirect product(C2×C29)⋊(C32×C5⋊D5)

Splittings

Fitting, socleC2×C32×C52×C29 ⋊ C2
derived, HallC52×C29 ⋊ C22×C32
HallC32×C52×C29 ⋊ C22
HallC32×C29 ⋊ C2×C5⋊D5
HallC32×C52 ⋊ C2×D29
SylowC29 ⋊ C2×C32×C5⋊D5
SylowC52 ⋊ C2×C32×D29

Subgroups

subgroupG/H
center, hypercenterC2×C32C5⋊D145
commutator, cosocle, hypocenterC52×C29C22×C32
FrattiniC1G
Fitting, socleC2×C32×C52×C29C2
LCSG ▷ C52×C29
UCSC1 ◁ C2×C32

480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 47
transitive degreeμt(G) = 13050

A minimal faithful permutation representation — 3 generators on 47 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)(31,32)(33,34)(36,37)(38,39)(43,44,45);(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)(35,36,38,39,37)(40,41,42)(46,47);(30,31,33,34,32)

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, 461);