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C4×(C61⋊C3)⋊C25 #32912880

order18300
automorphism?
homologyAbelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1

Aliases

direct productC4×(C61⋊C3)⋊C25
unambiguous semidirect product(C4×C61⋊C3)⋊C25
unambiguous semidirect product(C4×C61⋊C25)⋊C3

Splittings

derived, SylowC61 ⋊ C3×C4×C25
HallC4×C61⋊C25 ⋊ C3
HallC61⋊C25 ⋊ C3×C4
HallC4×C61⋊C3 ⋊ C25
HallC4×C61 ⋊ C3×C25
HallC61⋊C3 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC4×C5(C61⋊C3)⋊C5
commutator, hypocenterC61C3×C4×C25
FrattiniC2×C5C2×(C61⋊C3)⋊C5
FittingC4×C5×C61C3×C5
socle, cosocleC2×C5×C61C2×C3×C5
prime radicalC2×C5×C61⋊C3C2×C5
LCSG ▷ C61
UCSC1 ◁ C4×C5

36 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, 3);