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C25×C3⋊(C7⋊#261) #41031285

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

Aliases

direct productC25×C3⋊(C7⋊#261)
unambiguous semidirect productC3⋊(C25×C7⋊#261)
unambiguous semidirect productC7⋊(C25×C3⋊#261)

Splittings

Fitting, HallC3×C7×C13×C25 ⋊ C4
derived, HallC3×C7×C13 ⋊ C4×C25
HallC7×C13×C25 ⋊ Dic3
HallC3×C13×C25 ⋊ Dic7
HallC3×C7×C25 ⋊ #261
HallC13×C25 ⋊ Dic21
HallC7×C25 ⋊ C3⋊#261
HallC7×C13 ⋊ Dic3×C25
HallC3×C25 ⋊ C7⋊#261
HallC3×C13 ⋊ C25×Dic7
HallC3×C7 ⋊ C25×#261
SylowC13 ⋊ C25×Dic21
SylowC7 ⋊ C25×C3⋊#261
SylowC3 ⋊ C25×C7⋊#261

Subgroups

subgroupG/H
center, hypercenterC25C3⋊(C7⋊#261)
commutator, hypocenterC3×C7×C13C4×C25
FrattiniC5C5×C3⋊(C7⋊#261)
FittingC3×C7×C13×C25C4
socleC3×C5×C7×C13C4×C5
prime radical, cosocleC3×C5×C7×D13C2×C5
LCSG ▷ C3×C7×C13
UCSC1 ◁ C25

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6825

Conjugacy classes & character table

2175 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 175);