Finite Group Databasebeta

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C5×D3×C11×C17 #19150499

order5610
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C2×C5×C11×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×D3×C11×C17
unambiguous semidirect productC3⋊(C2×C5×C11×C17)

Splittings

Fitting, socle, HallC3×C5×C11×C17 ⋊ C2
derived, SylowC3 ⋊ C2×C5×C11×C17
HallC3×C11×C17 ⋊ C2×C5
HallC3×C5×C17 ⋊ C2×C11
HallC3×C5×C11 ⋊ C2×C17
HallC3×C17 ⋊ C2×C5×C11
HallC3×C11 ⋊ C2×C5×C17
HallC3×C5 ⋊ C2×C11×C17

Subgroups

subgroupG/H
center, hypercenterC5×C11×C17D3
commutator, hypocenterC3C2×C5×C11×C17
FrattiniC1G
Fitting, socleC3×C5×C11×C17C2
LCSG ▷ C3
UCSC1 ◁ C5×C11×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2805 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D3×C11×D17, C5×D3×C17×D11, C5×D3×D187, …
maximal normal subgroup ofC5×D3×C11×D17, C5×D3×C17×D11, C5×D3×D187, …
maximal quotient ofC5×C11×Dic3×C17, C2×C5×D3×C11×C17, C5×C11×C17×D9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5610, 10);