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C3×#87822 #11925314

order1200
isoclinismisoclinic class of #6053
automorphism?
homologyAbelianization (H1) = C3×C16 · Schur multiplier (H2) = C1

Aliases

direct productC3×#87822

Splittings

derived, SylowC52 ⋊ C3×C16
HallC3×C52 ⋊ C16

Subgroups

subgroupG/H
center, hypercenterC2×C3#6053
commutator, hypocenterC52C3×C16
FrattiniC2C3×#6053
Fitting, socle, prime radicalC2×C3×C52C8
cosocle#6033C2×C3
LCSG ▷ C52
UCSC1 ◁ C2×C3

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 2 generators on 29 points:

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

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 524);