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C25×C22⋊(C61⋊C3) #32912940

order18300
automorphism?
homologyAbelianization (H1) = C3×C25 · Schur multiplier (H2) = C2

Aliases

direct productC25×C22⋊(C61⋊C3)
unambiguous semidirect productC22⋊(C25×C61⋊C3)
unambiguous semidirect product(C22×C25)⋊(C61⋊C3)
unambiguous semidirect product(C25×C61)⋊A4

Splittings

Fitting, HallC22×C25×C61 ⋊ C3
derived, HallC22×C61 ⋊ C3×C25
HallC25×C61 ⋊ A4
HallC22×C25 ⋊ C61⋊C3
SylowC61 ⋊ A4×C25
SylowC22 ⋊ C25×C61⋊C3

Subgroups

subgroupG/H
center, hypercenterC25C22⋊(C61⋊C3)
commutator, hypocenterC22×C61C3×C25
FrattiniC5C5×C22⋊(C61⋊C3)
FittingC22×C25×C61C3
socle, cosocleC22×C5×C61C3×C5
prime radicalC5×C22⋊(C61⋊C3)C5
LCSG ▷ C22×C61
UCSC1 ◁ C25

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6100

Conjugacy classes & character table

2100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18300, 63);