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C3×C5⋊D5×D31 #22604898

order9300
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5

Aliases

direct productC3×C5⋊D5×D31

Splittings

Fitting, socle, HallC3×C52×C31 ⋊ C22
derived, HallC52×C31 ⋊ C22×C3
HallC3×C31 ⋊ C2×C5⋊D5
HallC3×C52 ⋊ C2×D31
SylowC31 ⋊ C2×C3×C5⋊D5
SylowC52 ⋊ C2×C3×D31

Subgroups

subgroupG/H
center, hypercenterC3C5⋊D5×D31
commutator, hypocenterC52×C31C22×C3
FrattiniC1G
Fitting, socleC3×C52×C31C22
LCSG ▷ C52×C31
UCSC1 ◁ C3

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

714 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5⋊D5×D31⋊C9, D31⋊((C5⋊D5)⋊C9), D31×(C5⋊D5)⋊C9, …
maximal normal subgroup ofC5⋊D5×D31⋊C9, D31⋊((C5⋊D5)⋊C9), D31×(C5⋊D5)⋊C9, …
maximal quotient ofC9×C5⋊D5×D31, C32×C5⋊D5×D31, C3×D31×C3⋊(C5⋊D5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9300, 172);