Finite Group Databasebeta

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C7×C25×C3⋊#261 #41031283

order27300
automorphism?
homologyAbelianization (H1) = C4×C7×C25 · Schur multiplier (H2) = C1

Aliases

direct productC7×C25×C3⋊#261
unambiguous semidirect productC3⋊(C7×C25×#261)

Splittings

Fitting, HallC3×C7×C13×C25 ⋊ C4
derived, HallC3×C13 ⋊ C4×C7×C25
HallC7×C13×C25 ⋊ Dic3
HallC3×C13×C25 ⋊ C4×C7
HallC3×C7×C25 ⋊ #261
HallC13×C25 ⋊ C7×Dic3
HallC3×C7×C13 ⋊ C4×C25
HallC7×C13 ⋊ Dic3×C25
HallC3×C25 ⋊ C7×#261
HallC3×C7 ⋊ C25×#261
SylowC13 ⋊ C7×Dic3×C25
SylowC3 ⋊ C7×C25×#261

Subgroups

subgroupG/H
center, hypercenterC7×C25C3⋊#261
commutator, hypocenterC3×C13C4×C7×C25
FrattiniC5C5×C7×C3⋊#261
FittingC3×C7×C13×C25C4
socleC3×C5×C7×C13C4×C5
prime radicalC3×C5×C7×D13C2×C5
cosocleC3×C5×D13C2×C5×C7
LCSG ▷ C3×C13
UCSC1 ◁ C7×C25

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6825

Conjugacy classes & character table

2625 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 173);