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C3×C22⋊D25 #10597038

order600
isoclinismisoclinic class of Dic50
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×C22⋊D25

Splittings

FittingC22×C3×C25 ⋊ C2
HallC3×C25 ⋊ D4
SylowC25 ⋊ C3×D4

Subgroups

subgroupG/H
centerC2×C3C2×D25
commutator, cosocleC2×C25C22×C3
FrattiniC2×C5C2×C3×D5
FittingC22×C3×C25C2
socleC2×C3×C5C2×D5
hypercenterC22×C3D25
hypocenterC25C3×D4
LCSG ▷ C2×C25 ▷ C25
UCSC1 ◁ C2×C3 ◁ C22×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 300

A minimal faithful permutation representation — 2 generators on 32 points:

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

Conjugacy classes & character table

159 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11924925, #11924926, D3×C22⋊D25, …
maximal normal subgroup of#11924925, #11924926, D3×C22⋊D25, …
maximal quotient ofC3×#87718, C3×#87720, C3×#87721, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(600, 19);