Finite Group Databasebeta

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C25×C22⋊#63270 #41031330

order27300
automorphism?
homologyAbelianization (H1) = C3×C25 · Schur multiplier (H2) = C2

Aliases

direct productC25×C22⋊#63270
unambiguous semidirect productC22⋊(C25×#63270)
unambiguous semidirect product(C22×C25)⋊#63270

Splittings

Fitting, HallC22×C7×C13×C25 ⋊ C3
derived, HallC22×C7×C13 ⋊ C3×C25
HallC7×C13×C25 ⋊ A4
HallC22×C13×C25 ⋊ ΓL(1,𝔽8)
HallC22×C7×C25 ⋊ C13⋊C3
HallC13×C25 ⋊ C22⋊ΓL(1,𝔽8)
HallC7×C25 ⋊ C22⋊(C13⋊C3)
HallC22×C25 ⋊ #63270
HallC7×C13 ⋊ A4×C25
HallC22×C13 ⋊ ΓL(1,𝔽8)×C25
HallC22×C7 ⋊ C25×C13⋊C3
SylowC13 ⋊ C25×C22⋊ΓL(1,𝔽8)
SylowC7 ⋊ C25×C22⋊(C13⋊C3)
SylowC22 ⋊ C25×#63270

Subgroups

subgroupG/H
center, hypercenterC25C22⋊#63270
commutator, hypocenterC22×C7×C13C3×C25
FrattiniC5C5×C22⋊#63270
FittingC22×C7×C13×C25C3
socle, cosocleC22×C5×C7×C13C3×C5
prime radicalC5×C22⋊#63270C5
LCSG ▷ C22×C7×C13
UCSC1 ◁ C25

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9100

Conjugacy classes & character table

3100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 220);