Finite Group Databasebeta

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C3×C7×C11×#595 #30628123

order15708
isoclinismisoclinic class of #595
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C11×#595

Splittings

Fitting, socle, HallC3×C7×C11×C17 ⋊ C4
derived, SylowC17 ⋊ C3×C4×C7×C11
HallC7×C11×C17 ⋊ C3×C4
HallC3×C11×C17 ⋊ C4×C7
HallC3×C7×C17 ⋊ C4×C11
HallC11×C17 ⋊ C3×C4×C7
HallC7×C17 ⋊ C3×C4×C11
HallC3×C17 ⋊ C4×C7×C11

Subgroups

subgroupG/H
center, hypercenterC3×C7×C11#595
commutator, hypocenterC17C3×C4×C7×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C17C4
prime radicalC3×C7×C11×D17C2
cosocleD17C2×C3×C7×C11
LCSG ▷ C17
UCSC1 ◁ C3×C7×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3927

Conjugacy classes & character table

1848 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15708, 44);