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C29×Dic225 #39907773

order26100
automorphism?
homologyAbelianization (H1) = C4×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×Dic225
unambiguous semidirect productC9⋊(C29×Dic25)

Splittings

derived, HallC9×C25 ⋊ C4×C29
HallC9×C25×C29 ⋊ C4
HallC25×C29 ⋊ Dic9
HallC9×C29 ⋊ Dic25
SylowC25 ⋊ C29×Dic9
SylowC9 ⋊ C29×Dic25

Subgroups

subgroupG/H
center, hypercenterC2×C29D225
commutator, hypocenterC9×C25C4×C29
FrattiniC2×C3×C5C29×D15
FittingC2×C9×C25×C29C2
socle, prime radicalC2×C3×C5×C29D15
cosocleC2×C9×C25C2×C29
LCSG ▷ C9×C25
UCSC1 ◁ C2×C29

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 26100

Conjugacy classes & character table

6612 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26100, 7);