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Cayley diagram

#2875⋊C3 #73226

order384
automorphism?
homologyAbelianization (H1) = C3×C42 · Schur multiplier (H2) = C4

Aliases

unambiguous semidirect product#2875⋊C3

Splittings

Fitting, Sylow#2875 ⋊ C3

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×A4
commutator, hypocenterQ8C3×C42
Fitting#2875C3
socleC22C2×C4×A4
prime radicalC2×#41⋊C3C22
cosocleC2×#41C22×C3
hypercenter#97A4
LCSG ▷ Q8
UCSC1 ◁ C2×C4 ◁ #97

151 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 128

A minimal faithful permutation representation — 2 generators on 36 points:

(1,2,3,4)(6,11)(8,18,19)(9,21,20)(12,22)(13,14,27,23,24,28)(15,29,30)(16,32,31)(25,26,35,33,34,36);(5,28,17,35,10,27,7,36)(6,32,22,21,11,30,12,19)(8,14,31,34,20,24,15,26)(9,23,29,25,18,13,16,33)

Polycyclic presentation:

2^2,3,2^5|a^2=d,b^2=e,d^2=h,f^2=h,g^2=h,b^a=bh,f^c=gh,g^c=fgh,g^f=gh

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#17654⋊C3, #17655⋊C3, #33329⋊C3, …
maximal normal subgroup of#17654⋊C3, #17655⋊C3, #33329⋊C3, …
maximal quotient of#17316⋊C3, #17320⋊C3, #20336⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 5802);