Finite Group Databasebeta

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C2×C3×C5⋊D155 #22604941

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

Aliases

direct productC2×C3×C5⋊D155
unambiguous semidirect product(C2×C5)⋊(C3×D155)

Splittings

Fitting, socleC2×C3×C52×C31 ⋊ C2
derived, HallC52×C31 ⋊ C22×C3
HallC3×C52×C31 ⋊ C22
HallC3×C31 ⋊ C2×C5⋊D5
HallC3×C52 ⋊ C2×D31
SylowC31 ⋊ C2×C3×C5⋊D5
SylowC52 ⋊ C2×C3×D31

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊D155
commutator, hypocenterC52×C31C22×C3
FrattiniC1G
Fitting, socleC2×C3×C52×C31C2
LCSG ▷ C52×C31
UCSC1 ◁ C2×C3

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2334 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5⋊(C5⋊(D31⋊C9)), C2×#28358426, C2×#28358428, …
maximal normal subgroup ofC2×C5⋊(C5⋊(D31⋊C9)), C2×#28358426, C2×#28358428, …
maximal quotient ofC2×C9×C5⋊D155, C3×D3×C5⋊D155, C2×C32×C5⋊D155, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9300, 215);