Finite Group Databasebeta

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C2×C3×C7×C25×D13 #41031332

order27300
automorphism?
homologyAbelianization (H1) = C22×C3×C7×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C7×C25×D13

Splittings

FittingC2×C3×C7×C13×C25 ⋊ C2
derived, SylowC13 ⋊ C22×C3×C7×C25
HallC3×C7×C13×C25 ⋊ C22
HallC7×C13×C25 ⋊ C22×C3
HallC3×C13×C25 ⋊ C22×C7
HallC13×C25 ⋊ C22×C3×C7
HallC3×C7×C13 ⋊ C22×C25
HallC7×C13 ⋊ C22×C3×C25
HallC3×C13 ⋊ C22×C7×C25

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7×C25D13
commutator, hypocenterC13C22×C3×C7×C25
FrattiniC5C2×C3×C5×C7×D13
FittingC2×C3×C7×C13×C25C2
socleC2×C3×C5×C7×C13C2×C5
prime radicalC2×C3×C5×C7×D13C5
cosocleC5×C13C22×C3×C5×C7
LCSG ▷ C13
UCSC1 ◁ C2×C3×C7×C25

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13650

Conjugacy classes & character table

8400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 222);