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C3×C5⋊D5×D29 #22576453

order8700
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5

Aliases

direct productC3×C5⋊D5×D29
unambiguous semidirect product(C5×D29)⋊(C3×D5)

Splittings

Fitting, socle, HallC3×C52×C29 ⋊ C22
derived, HallC52×C29 ⋊ C22×C3
HallC3×C29 ⋊ C2×C5⋊D5
HallC3×C52 ⋊ C2×D29
SylowC29 ⋊ C2×C3×C5⋊D5
SylowC52 ⋊ C2×C3×D29

Subgroups

subgroupG/H
center, hypercenterC3C5⋊D5×D29
commutator, hypocenterC52×C29C22×C3
FrattiniC1G
Fitting, socleC3×C52×C29C22
LCSG ▷ C52×C29
UCSC1 ◁ C3

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

672 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD29×(C5⋊D5)⋊C9, C9×C5⋊D5×D29, C3×D29×(C5⋊D5)⋊C3, …
maximal normal subgroup ofD29×(C5⋊D5)⋊C9, C9×C5⋊D5×D29, C3×D29×(C5⋊D5)⋊C3, …
maximal quotient ofC9×C5⋊D5×D29, C32×C5⋊D5×D29, C3×D29×C3⋊(C5⋊D5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8700, 95);