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C2×C3⋊(C5⋊D155) #22604935

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

Aliases

direct productC2×C3⋊(C5⋊D155)
unambiguous semidirect product(C2×C3)⋊(C5⋊D155)
unambiguous semidirect product(C2×C5)⋊D465
unambiguous semidirect product(C2×C31)⋊(C3⋊(C5⋊D5))

Splittings

Fitting, socleC2×C3×C52×C31 ⋊ C2
derived, HallC3×C52×C31 ⋊ C22
HallC52×C31 ⋊ C2×D3
HallC3×C31 ⋊ C2×C5⋊D5
HallC3×C52 ⋊ C2×D31
SylowC31 ⋊ C2×C3⋊(C5⋊D5)
SylowC52 ⋊ C2×D93
SylowC3 ⋊ C2×C5⋊D155

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C5⋊D155)
commutator, hypocenterC3×C52×C31C22
FrattiniC1G
Fitting, socleC2×C3×C52×C31C2
LCSG ▷ C3×C52×C31
UCSC1 ◁ C2

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2328 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5⋊D1395, C2×C3⋊#17987869, C2×C3⋊#17987871, …
maximal normal subgroup ofC2×C3⋊#17987869, C2×C3⋊#17987871, C2×C3⋊(C5⋊(C5⋊(D31⋊C3))), …
maximal quotient ofC2×C5⋊D1395, D3×C3⋊(C5⋊D155), C2×C3×C3⋊(C5⋊D155), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9300, 209);