Finite Group Databasebeta

← Prev (#10597023) Next (#10597025) →

C3×#6016 #10597024

order600
isoclinismisoclinic class of #1035
automorphism?
homologyAbelianization (H1) = C3×C8 · Schur multiplier (H2) = C1

Aliases

direct productC3×#6016

Splittings

derived, SylowC25 ⋊ C3×C8
HallC3×C25 ⋊ C8

Subgroups

subgroupG/H
center, hypercenterC2×C3#1035
commutator, hypocenterC25C3×C8
FrattiniC2×C5C3×AGL(1,𝔽5)
FittingC2×C3×C25C4
socle, prime radicalC2×C3×C5AGL(1,𝔽5)
cosocleDic25C2×C3
LCSG ▷ C25
UCSC1 ◁ C2×C3

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 600

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

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

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11924879, #11924880, D3×#6016, …
maximal normal subgroup of#11924879, #11924880, D3×#6016, …
maximal quotient ofC3×#87709, C2×C3×#6016, C9×#6016, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(600, 5);