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(C31⋊C3)⋊#261 #18012831

order4836
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product(C31⋊C3)⋊#261

Splittings

Fitting, socle, derived, HallC13×C31 ⋊ C3×C4
HallC31⋊#261 ⋊ C3
HallC13×C31⋊C3 ⋊ C4
HallC31⋊C3 ⋊ #261
SylowC31 ⋊ C3×#261
SylowC13 ⋊ (C31⋊C3)⋊C4

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC13×C31C3×C4
prime radicalD13×C31⋊C3C2
cosocleD13×C31C2×C3
LCSG ▷ C13×C31
UCSC1

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 44
transitive degreeμt(G) = 403

Polycyclic presentation:

2,3,2,13,31|a^2=c,d^a=d^5,e^a=e^30,e^b=e^5,d^c=d^12

Conjugacy classes & character table

61 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C31⋊C3)⋊AGL(1,𝔽13), C3×(C31⋊C3)⋊#261, C3⋊((C31⋊C3)⋊#261), …
maximal normal subgroup of(C31⋊C3)⋊AGL(1,𝔽13), C3×(C31⋊C3)⋊#261, ((C31⋊C3)⋊C5)⋊#261, …
maximal quotient of(C31⋊C9)⋊#261, C3×(C31⋊C3)⋊#261, C3⋊((C31⋊C3)⋊#261), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4836, 35);