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C25×Dic61⋊C3 #32912884

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

Aliases

direct productC25×Dic61⋊C3
unambiguous semidirect product(C25×Dic61)⋊C3

Splittings

derived, SylowC61 ⋊ C3×C4×C25
HallC25×Dic61 ⋊ C3
HallC25×C61⋊C3 ⋊ C4
HallC25×C61 ⋊ C3×C4
HallDic61 ⋊ C3×C25
HallC61⋊C3 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC2×C25D61⋊C3
commutator, hypocenterC61C3×C4×C25
FrattiniC2×C5C5×D61⋊C3
FittingC2×C25×C61C2×C3
socle, cosocleC2×C5×C61C2×C3×C5
prime radicalC2×C5×C61⋊C3C2×C5
LCSG ▷ C61
UCSC1 ◁ C2×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6100

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18300, 7);