Finite Group Databasebeta

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C32×#4094 #13087873

order1440
automorphism?
homologyAbelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C22×C3

Aliases

direct productC32×#4094

Splittings

HallC32×C5 ⋊ #131
SylowC5 ⋊ C32×#131

Subgroups

subgroupG/H
centerC32×C4C22×D5
commutatorC2×C5C22×C32×C4
FrattiniC4C22×C32×D5
Fitting, prime radicalC32×C5×#41C2
socleC2×C32×C5C22×C4
cosocleC4×C5C23×C32
hypercenterC32×#41D5
hypocenterC5C32×#131
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C32×C4 ◁ C32×#41

372 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 27
transitive degreeμt(G) = 720

A minimal faithful permutation representation — 3 generators on 27 points:

(1,2,3)(7,8,10,11,9)(14,20)(17,23)(21,26)(24,27);(4,5,6)(12,14)(13,17)(15,21)(16,20)(18,24)(19,23)(22,26)(25,27);(8,9)(10,11)(12,13,15,18,16,19,22,25)(14,17,21,24,20,23,26,27)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4190);