Finite Group Databasebeta

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C22×C25×#63271 #41031326

order27300
automorphism?
homologyAbelianization (H1) = C22×C3×C25 · Schur multiplier (H2) = C2

Aliases

direct productC22×C25×#63271

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC22×C25#63271
commutator, hypocenterC7×C13C22×C3×C25
FrattiniC5C22×C5×#63271
FittingC22×C7×C13×C25C3
socleC22×C5×C7×C13C3×C5
prime radicalC22×C5×#63271C5
cosocleC5×C7×C13C22×C3×C5
LCSG ▷ C7×C13
UCSC1 ◁ C22×C25

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9100

Conjugacy classes & character table

3300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 216);