Finite Group Databasebeta

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C32×C25×Dic29 #39907804

order26100
automorphism?
homologyAbelianization (H1) = C32×C4×C25 · Schur multiplier (H2) = C3

Aliases

direct productC32×C25×Dic29

Splittings

derived, SylowC29 ⋊ C32×C4×C25
HallC32×C25×C29 ⋊ C4
HallC25×C29 ⋊ C32×C4
HallC32×C29 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC2×C32×C25D29
commutator, hypocenterC29C32×C4×C25
FrattiniC2×C5C32×C5×D29
FittingC2×C32×C25×C29C2
socle, prime radicalC2×C32×C5×C29C2×C5
cosocleC2×C5×C29C2×C32×C5
LCSG ▷ C29
UCSC1 ◁ C2×C32×C25

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 26100

Conjugacy classes & character table

7200 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26100, 38);