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#20300038⋊C5 #49137344

order36300
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product#20300038⋊C5

Splittings

Fitting, socleC5×C112 ⋊ C5×Dic3
derivedC5×C112⋊C3 ⋊ C4×C5
HallC5×(C112⋊C3)⋊C5 ⋊ C4
HallC5×#10597243 ⋊ Dic3
HallC112⋊C3 ⋊ C5×AGL(1,𝔽5)
SylowC112 ⋊ C5×ΓL(1,𝔽16)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, hypocenterC5×C112⋊C3C4×C5
Fitting, socleC5×C112C5×Dic3
prime radicalC5⋊(((C11⋊D11)⋊C3)⋊C5)C2
cosocleC5⋊((C11⋊D11)⋊C3)C2×C5
LCSG ▷ C5×C112⋊C3
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 330

Polycyclic presentation:

2,5,2,3,5,11^2|a^2=c,d^a=d^2,e^a=e^2,f^a=f^10g^7,g^a=f^6g,f^b=f^4,g^b=g^4,e^c=e^4,f^c=f^10,g^c=g^10,f^d=f^5g^7,g^d=f^5g^5

Conjugacy classes & character table

55 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 480);