Finite Group Databasebeta

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C22×C5×(C112⋊C3)⋊C5 #49137544

order36300
automorphism?
homologyAbelianization (H1) = C22×C3×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC22×C5×(C112⋊C3)⋊C5
unambiguous semidirect product(C22×C112⋊C3)⋊C52
unambiguous semidirect product(C22×C5×C112⋊C3)⋊C5

Splittings

Fitting, socleC22×C5×C112 ⋊ C3×C5
derived, SylowC112 ⋊ C22×C3×C52
HallC22×C5×#10597243 ⋊ C3
HallC5×#10597243 ⋊ C22×C3
HallC22×C112⋊C3 ⋊ C52
HallC22×C112 ⋊ C3×C52
HallC112⋊C3 ⋊ C22×C52

Subgroups

subgroupG/H
center, hypercenterC22×C5(C112⋊C3)⋊C5
commutator, cosocle, hypocenterC112C22×C3×C52
FrattiniC1G
Fitting, socleC22×C5×C112C3×C5
LCSG ▷ C112
UCSC1 ◁ C22×C5

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 660

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 680);