Finite Group Databasebeta

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C3×C5×C11×#3866 #37567571

order24420
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C11×#3866

Splittings

Fitting, socle, HallC3×C5×C11×C37 ⋊ C4
derived, SylowC37 ⋊ C3×C4×C5×C11
HallC5×C11×C37 ⋊ C3×C4
HallC3×C11×C37 ⋊ C4×C5
HallC3×C5×C37 ⋊ C4×C11
HallC11×C37 ⋊ C3×C4×C5
HallC5×C37 ⋊ C3×C4×C11
HallC3×C37 ⋊ C4×C5×C11

Subgroups

subgroupG/H
center, hypercenterC3×C5×C11#3866
commutator, hypocenterC37C3×C4×C5×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C37C4
prime radicalC3×C5×C11×D37C2
cosocleD37C2×C3×C5×C11
LCSG ▷ C37
UCSC1 ◁ C3×C5×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6105

Conjugacy classes & character table

2145 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 92);