Finite Group Databasebeta

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C3×C23×C5⋊D55 #49182152

order37950
automorphism?
homologyAbelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C5

Aliases

direct productC3×C23×C5⋊D55
unambiguous semidirect productC5⋊(C3×C23×D55)
unambiguous semidirect productC11⋊(C3×C23×C5⋊D5)

Splittings

Fitting, socle, HallC3×C52×C11×C23 ⋊ C2
derived, HallC52×C11 ⋊ C2×C3×C23
HallC52×C11×C23 ⋊ C2×C3
HallC3×C52×C23 ⋊ D11
HallC3×C52×C11 ⋊ C2×C23
HallC3×C11×C23 ⋊ C5⋊D5
HallC52×C23 ⋊ C3×D11
HallC11×C23 ⋊ C3×C5⋊D5
HallC3×C52 ⋊ D11×C23
HallC3×C11 ⋊ C23×C5⋊D5
SylowC52 ⋊ C3×D11×C23
SylowC11 ⋊ C3×C23×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC3×C23C5⋊D55
commutator, cosocle, hypocenterC52×C11C2×C3×C23
FrattiniC1G
Fitting, socleC3×C52×C11×C23C2
LCSG ▷ C52×C11
UCSC1 ◁ C3×C23

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18975

Conjugacy classes & character table

9591 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37950, 89);