Finite Group Databasebeta

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C2×C3×C52×D77 #37528739

order23100
automorphism?
homologyAbelianization (H1) = C22×C3×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C3×C52×D77

Splittings

Fitting, socleC2×C3×C52×C7×C11 ⋊ C2
derived, HallC7×C11 ⋊ C22×C3×C52
HallC3×C52×C7×C11 ⋊ C22
HallC52×C7×C11 ⋊ C22×C3
HallC3×C52×C11 ⋊ C2×D7
HallC3×C52×C7 ⋊ C2×D11
HallC52×C11 ⋊ C2×C3×D7
HallC3×C7×C11 ⋊ C22×C52
HallC52×C7 ⋊ C2×C3×D11
HallC3×C11 ⋊ C2×C52×D7
HallC3×C7 ⋊ C2×C52×D11
SylowC11 ⋊ C2×C3×C52×D7
SylowC7 ⋊ C2×C3×C52×D11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C52D77
commutator, cosocle, hypocenterC7×C11C22×C3×C52
FrattiniC1G
Fitting, socleC2×C3×C52×C7×C11C2
LCSG ▷ C7×C11
UCSC1 ◁ C2×C3×C52

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11550

Conjugacy classes & character table

6000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 550);