Finite Group Databasebeta

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C4×C5×#14274262 #50303676

order38220
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×#14274262

Splittings

Fitting, HallC4×C5×C72×C13 ⋊ C3
derived, HallC72×C13 ⋊ C3×C4×C5
HallC5×C72×C13 ⋊ C3×C4
HallC4×C72×C13 ⋊ C3×C5
HallC4×C5×C72 ⋊ C13⋊C3
HallC4×C5×C13 ⋊ #3861
HallC5×C72 ⋊ C4×C13⋊C3
HallC4×C72 ⋊ C5×C13⋊C3
HallC5×C13 ⋊ C4×#3861
HallC4×C13 ⋊ C5×#3861
SylowC72 ⋊ C4×C5×C13⋊C3
SylowC13 ⋊ C4×C5×#3861

Subgroups

subgroupG/H
center, hypercenterC4×C5#14274262
commutator, hypocenterC72×C13C3×C4×C5
FrattiniC2C2×C5×#14274262
FittingC4×C5×C72×C13C3
socleC2×C5×C72×C13C2×C3
prime radicalC2×C5×#14274262C2
cosocleC2×C72×C13C2×C3×C5
LCSG ▷ C72×C13
UCSC1 ◁ C4×C5

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 12740

A minimal faithful permutation representation — 3 generators on 36 points:

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

Conjugacy classes & character table

4300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 362);