Finite Group Databasebeta

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C9×C25×#1181 #39907776

order26100
automorphism?
homologyAbelianization (H1) = C4×C9×C25 · Schur multiplier (H2) = C1

Aliases

direct productC9×C25×#1181

Splittings

Fitting, HallC9×C25×C29 ⋊ C4
derived, SylowC29 ⋊ C4×C9×C25
HallC25×C29 ⋊ C4×C9
HallC9×C29 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC9×C25#1181
commutator, hypocenterC29C4×C9×C25
FrattiniC3×C5C3×C5×#1181
FittingC9×C25×C29C4
socleC3×C5×C29C3×C4×C5
prime radical, cosocleC3×C5×D29C2×C3×C5
LCSG ▷ C29
UCSC1 ◁ C9×C25

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6525

Conjugacy classes & character table

2475 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26100, 10);