Finite Group Databasebeta

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C22×C5×C11×C37⋊C3 #37567632

order24420
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC22×C5×C11×C37⋊C3

Splittings

Fitting, socle, HallC22×C5×C11×C37 ⋊ C3
derived, SylowC37 ⋊ C22×C3×C5×C11
HallC5×C11×C37 ⋊ C22×C3
HallC22×C11×C37 ⋊ C3×C5
HallC22×C5×C37 ⋊ C3×C11
HallC11×C37 ⋊ C22×C3×C5
HallC5×C37 ⋊ C22×C3×C11
HallC22×C37 ⋊ C3×C5×C11

Subgroups

subgroupG/H
center, hypercenterC22×C5×C11C37⋊C3
commutator, cosocle, hypocenterC37C22×C3×C5×C11
FrattiniC1G
Fitting, socleC22×C5×C11×C37C3
LCSG ▷ C37
UCSC1 ◁ C22×C5×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8140

Conjugacy classes & character table

3300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 153);