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D13×#3861 #16838475

order3822
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productD13×#3861

Splittings

Fitting, socle, derived, HallC72×C13 ⋊ C2×C3
HallC13×#3861 ⋊ C2
HallC72×D13 ⋊ C3
SylowC72 ⋊ C3×D13
SylowC13 ⋊ C2×#3861

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC72×C13C2×C3
LCSG ▷ C72×C13
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 27
transitive degreeμt(G) = 637

A minimal faithful permutation representation — 3 generators on 27 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD13⋊C3×#3861, #26039554, ΓL(1,𝔽8)2×D13, …
maximal normal subgroup ofD13⋊C3×#3861, #26039554, ΓL(1,𝔽8)2×D13, …
maximal quotient ofD13×#89204, C3×D13×#3861, D39×#3861, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3822, 68);