Finite Group Databasebeta

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C3×C25×Dic59 #31799141

order17700
isoclinismisoclinic class of D59
automorphism?
homologyAbelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×C25×Dic59
unambiguous semidirect productC59⋊(C3×C4×C25)

Splittings

derived, SylowC59 ⋊ C3×C4×C25
HallC3×C25×C59 ⋊ C4
HallC25×C59 ⋊ C3×C4
HallC3×C59 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC2×C3×C25D59
commutator, hypocenterC59C3×C4×C25
FrattiniC2×C5C3×C5×D59
FittingC2×C3×C25×C59C2
socle, prime radicalC2×C3×C5×C59C2×C5
cosocleC2×C5×C59C2×C3×C5
LCSG ▷ C59
UCSC1 ◁ C2×C3×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17700

Conjugacy classes & character table

4650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17700, 2);