Finite Group Databasebeta

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C25×D13×D21 #41031286

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

Aliases

direct productC25×D13×D21
unambiguous semidirect product(C3×D13)⋊(D7×C25)
unambiguous semidirect product(C7×D13)⋊(D3×C25)

Splittings

Fitting, HallC3×C7×C13×C25 ⋊ C22
derived, HallC3×C7×C13 ⋊ C22×C25
HallC7×C13×C25 ⋊ C2×D3
HallC3×C13×C25 ⋊ C2×D7
HallC3×C7×C25 ⋊ C2×D13
HallC13×C25 ⋊ C2×D21
HallC7×C25 ⋊ D3×D13
HallC7×C13 ⋊ C2×D3×C25
HallC3×C25 ⋊ D7×D13
HallC3×C13 ⋊ C2×D7×C25
HallC3×C7 ⋊ C2×C25×D13
SylowC13 ⋊ C2×C25×D21
SylowC7 ⋊ D3×C25×D13
SylowC3 ⋊ D7×C25×D13

Subgroups

subgroupG/H
center, hypercenterC25D13×D21
commutator, hypocenterC3×C7×C13C22×C25
FrattiniC5C5×D13×D21
FittingC3×C7×C13×C25C22
socle, cosocleC3×C5×C7×C13C22×C5
prime radicalC5×D13×D21C5
LCSG ▷ C3×C7×C13
UCSC1 ◁ C25

120 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6825

Conjugacy classes & character table

2400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 176);