Finite Group Databasebeta

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C3×C5×C11×Dic13 #22575033

order8580
isoclinismisoclinic class of D13
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C11×Dic13

Splittings

derived, SylowC13 ⋊ C3×C4×C5×C11
HallC3×C5×C11×C13 ⋊ C4
HallC5×C11×C13 ⋊ C3×C4
HallC3×C11×C13 ⋊ C4×C5
HallC3×C5×C13 ⋊ C4×C11
HallC11×C13 ⋊ C3×C4×C5
HallC5×C13 ⋊ C3×C4×C11
HallC3×C13 ⋊ C4×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C11D13
commutator, hypocenterC13C3×C4×C5×C11
FrattiniC2C3×C5×C11×D13
Fitting, socleC2×C3×C5×C11×C13C2
LCSG ▷ C13
UCSC1 ◁ C2×C3×C5×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2640 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C9×C11×Dic13, C5×C11×Dic13⋊C9, C3×C5×C11×Dic13⋊C3, …
maximal normal subgroup ofC5×C9×C11×Dic13, C5×C11×Dic13⋊C9, C3×C5×C11×Dic13⋊C3, …
maximal quotient ofC5×C9×C11×Dic13, C3×C5×C11×Dic39, C32×C5×C11×Dic13

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 5);