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Dic5×ΓL(1,𝔽32)⋊C9 #42124342

order27900
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productDic5×ΓL(1,𝔽32)⋊C9
unambiguous semidirect product(Dic5×ΓL(1,𝔽32))⋊C9
unambiguous semidirect product(Dic5×C31⋊C9)⋊C5

Splittings

derivedC5×C31 ⋊ C4×C5×C9
HallC5×ΓL(1,𝔽32)⋊C9 ⋊ C4
HallDic5×ΓL(1,𝔽32) ⋊ C9
HallC5×ΓL(1,𝔽32) ⋊ C4×C9
HallC31⋊C9 ⋊ C5×Dic5
SylowC31 ⋊ C5×C9×Dic5

Subgroups

subgroupG/H
center, Frattini, hypercenterC2×C3D5×(C31⋊C3)⋊C5
commutator, hypocenterC5×C31C4×C5×C9
Fitting, socle, cosocleC2×C3×C5×C31C2×C3×C5
prime radicalC2×C3×C5×ΓL(1,𝔽32)C2×C3
LCSG ▷ C5×C31
UCSC1 ◁ C2×C3

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

408 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 89);