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C22×(C61⋊C3)⋊C25 #32912902

order18300
automorphism?
homologyAbelianization (H1) = C22×C3×C25 · Schur multiplier (H2) = C2

Aliases

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

Splittings

derived, SylowC61 ⋊ C22×C3×C25
HallC22×C61⋊C25 ⋊ C3
HallC61⋊C25 ⋊ C22×C3
HallC22×C61⋊C3 ⋊ C25
HallC22×C61 ⋊ C3×C25
HallC61⋊C3 ⋊ C22×C25

Subgroups

subgroupG/H
center, hypercenterC22×C5(C61⋊C3)⋊C5
commutator, hypocenterC61C22×C3×C25
FrattiniC5C22×(C61⋊C3)⋊C5
Fitting, socleC22×C5×C61C3×C5
prime radicalC22×C5×C61⋊C3C5
cosocleC5×C61C22×C3×C5
LCSG ▷ C61
UCSC1 ◁ C22×C5

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6100

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18300, 25);