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D13×C52⋊C3 #14519610

order1950
isoclinismisoclinic class of D13×C52⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C5

Aliases

direct productD13×C52⋊C3

Splittings

Fitting, socle, derived, HallC52×C13 ⋊ C2×C3
HallC13×C52⋊C3 ⋊ C2
HallC52×D13 ⋊ C3
SylowC52 ⋊ C3×D13
SylowC13 ⋊ C2×C52⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C13C2×C3
LCSG ▷ C52×C13
UCSC1

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 195

A minimal faithful permutation representation — 2 generators on 28 points:

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

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#16839100, D13×#3874, #16839115, …
maximal normal subgroup of#16839100, D13×#3874, #16839115, …
maximal quotient ofDic13×C52⋊C3, C2×D13×C52⋊C3, C7×D13×C52⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1950, 20);