Finite Group Databasebeta

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C3×D21×C11⋊C25 #46831409

order34650
automorphism?
homologyAbelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×D21×C11⋊C25
unambiguous semidirect productC3⋊(C3×D7×C11⋊C25)
unambiguous semidirect product(C3×C11×D21)⋊C25

Splittings

derivedC3×C7×C11 ⋊ C2×C3×C25
HallC32×C7×C11⋊C25 ⋊ C2
HallC32×C11⋊C25 ⋊ D7
HallC7×C11⋊C25 ⋊ C3×D3
HallC3×C11×D21 ⋊ C25
HallC32×C7×C11 ⋊ C2×C25
HallC32×C11 ⋊ D7×C25
HallC7×C11 ⋊ C3×D3×C25
HallC32×C7 ⋊ C2×C11⋊C25
SylowC11 ⋊ C3×C25×D21
SylowC32 ⋊ D7×C11⋊C25
SylowC7 ⋊ C3×D3×C11⋊C25

Subgroups

subgroupG/H
center, hypercenterC3×C5D21×C11⋊C5
commutator, hypocenterC3×C7×C11C2×C3×C25
FrattiniC5C3×D21×C11⋊C5
Fitting, socleC32×C5×C7×C11C2×C5
prime radicalC3×C5×C11×D21C5
cosocleC3×C5×C7×C11C2×C3×C5
LCSG ▷ C3×C7×C11
UCSC1 ◁ C3×C5

108 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 108 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11550

Conjugacy classes & character table

1260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 52);