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C32×Dic101⋊C5 #32911417

order18180
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×Dic101⋊C5
unambiguous semidirect productDic101⋊(C32×C5)
unambiguous semidirect product(C3×Dic101)⋊(C3×C5)
unambiguous semidirect product(C32×Dic101)⋊C5

Splittings

derived, SylowC101 ⋊ C32×C4×C5
HallC32×C101⋊C5 ⋊ C4
HallC32×Dic101 ⋊ C5
HallC32×C101 ⋊ C4×C5
HallC101⋊C5 ⋊ C32×C4
HallDic101 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C32D101⋊C5
commutator, hypocenterC101C32×C4×C5
FrattiniC2C32×D101⋊C5
Fitting, socleC2×C32×C101C2×C5
prime radicalC2×C32×C101⋊C5C2
cosocleC2×C101C2×C32×C5
LCSG ▷ C101
UCSC1 ◁ C2×C32

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3636

Conjugacy classes & character table

360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18180, 50);