Finite Group Databasebeta

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C52×D3×C11×C23 #49182154

order37950
automorphism?
homologyAbelianization (H1) = C2×C52×C11×C23 · Schur multiplier (H2) = C5

Aliases

direct productC52×D3×C11×C23
unambiguous semidirect productC3⋊(C2×C52×C11×C23)

Splittings

Fitting, socle, HallC3×C52×C11×C23 ⋊ C2
derived, SylowC3 ⋊ C2×C52×C11×C23
HallC3×C52×C23 ⋊ C2×C11
HallC3×C52×C11 ⋊ C2×C23
HallC3×C11×C23 ⋊ C2×C52
HallC3×C52 ⋊ C2×C11×C23
HallC3×C23 ⋊ C2×C52×C11
HallC3×C11 ⋊ C2×C52×C23

Subgroups

subgroupG/H
center, hypercenterC52×C11×C23D3
commutator, cosocle, hypocenterC3C2×C52×C11×C23
FrattiniC1G
Fitting, socleC3×C52×C11×C23C2
LCSG ▷ C3
UCSC1 ◁ C52×C11×C23

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18975

Conjugacy classes & character table

18975 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37950, 91);