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C3×#6014 #10597021

order600
isoclinismisoclinic class of D25
automorphism?
homologyAbelianization (H1) = C3×C8 · Schur multiplier (H2) = C1

Aliases

direct productC3×#6014

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3×C4D25
commutator, hypocenterC25C3×C8
FrattiniC4×C5C3×D5
FittingC3×C4×C25C2
socle, prime radicalC2×C3×C5Dic5
cosocleC4×C25C2×C3
LCSG ▷ C25
UCSC1 ◁ C3×C4

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

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#87709, C3⋊#87709, #11924798, …
maximal normal subgroup ofC3×#87709, C3⋊#87709, #11924798, …
maximal quotient ofC3×#87707, C2×C3×#6014, C9×#6014, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(600, 2);