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Cayley diagram

#2834⋊C3 #73208

order384
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product#2834⋊C3

Splittings

Fitting, Sylow#2834 ⋊ C3

Subgroups

subgroupG/H
center, hypercenterC2#560⋊C3
commutator, cosocle, hypocenter#95C22×C3
Frattini, socleC23C22×A4
Fitting#2834C3
prime radical#399⋊C3C2
LCSG ▷ #95
UCSC1 ◁ C2

97 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 48

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

(1,5,2)(3,16,7,9,15,4)(6,12,14,10,11,13)(19,25,28)(20,26,27)(22,29,32)(23,30,31);(1,11,5,15)(2,16,8,12)(3,14,9,4)(6,13,10,7)(17,29)(18,27)(19,32)(20,22)(21,31)(23,26)(24,25)(28,30)

Polycyclic presentation:

2^2,3,2^5|a^2=f,d^2=h,e^2=fg,c^a=cfgh,d^a=dfgh,e^a=efh,c^b=cfgh,d^b=dfh,e^b=eg,d^c=defgh,e^c=df,g^c=fh,h^c=gh,e^d=ef

Conjugacy classes & character table

30 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#2834⋊C3, #36676⋊C3, #52742⋊C3, …
maximal normal subgroup ofC2×#2834⋊C3, #36676⋊C3, #52742⋊C3, …
maximal quotient of#14636⋊C3, #14656⋊C3, #17114⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 5784);