Finite Group Databasebeta

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C3×C4×C71⋊C25 #36319010

order21300
automorphism?
homologyAbelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×C4×C71⋊C25
unambiguous semidirect product(C4×C71)⋊(C3×C25)
unambiguous semidirect product(C3×C4×C71)⋊C25

Splittings

derived, SylowC71 ⋊ C3×C4×C25
HallC3×C4×C71 ⋊ C25
HallC4×C71 ⋊ C3×C25
HallC3×C71 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5C71⋊C5
commutator, hypocenterC71C3×C4×C25
FrattiniC2×C5C2×C3×C71⋊C5
FittingC3×C4×C5×C71C5
socle, prime radicalC2×C3×C5×C71C2×C5
cosocleC2×C5×C71C2×C3×C5
LCSG ▷ C71
UCSC1 ◁ C3×C4×C5

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21300

Conjugacy classes & character table

1140 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21300, 2);