Finite Group Databasebeta

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C23×C25×Dic9 #35207889

order20700
automorphism?
homologyAbelianization (H1) = C4×C23×C25 · Schur multiplier (H2) = C1

Aliases

direct productC23×C25×Dic9
unambiguous semidirect productC9⋊(C4×C23×C25)

Splittings

derived, SylowC9 ⋊ C4×C23×C25
HallC9×C23×C25 ⋊ C4
HallC9×C25 ⋊ C4×C23
HallC9×C23 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC2×C23×C25D9
commutator, hypocenterC9C4×C23×C25
FrattiniC2×C3×C5C5×D3×C23
FittingC2×C9×C23×C25C2
socle, prime radicalC2×C3×C5×C23C5×D3
cosocleC2×C5×C9C2×C5×C23
LCSG ▷ C9
UCSC1 ◁ C2×C23×C25

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 20700

Conjugacy classes & character table

6900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20700, 5);