Finite Group Databasebeta

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C3×C72×D115 #46798972

order33810
automorphism?
homologyAbelianization (H1) = C2×C3×C72 · Schur multiplier (H2) = C7

Aliases

direct productC3×C72×D115
unambiguous semidirect productC5⋊(C3×C72×D23)
unambiguous semidirect productC23⋊(C3×C72×D5)

Splittings

Fitting, socle, HallC3×C5×C72×C23 ⋊ C2
derived, HallC5×C23 ⋊ C2×C3×C72
HallC5×C72×C23 ⋊ C2×C3
HallC3×C72×C23 ⋊ D5
HallC72×C23 ⋊ C3×D5
HallC3×C5×C72 ⋊ D23
HallC3×C5×C23 ⋊ C2×C72
HallC5×C72 ⋊ C3×D23
HallC3×C23 ⋊ C72×D5
SylowC23 ⋊ C3×C72×D5
HallC3×C5 ⋊ C72×D23
SylowC5 ⋊ C3×C72×D23

Subgroups

subgroupG/H
center, hypercenterC3×C72D115
commutator, cosocle, hypocenterC5×C23C2×C3×C72
FrattiniC1G
Fitting, socleC3×C5×C72×C23C2
LCSG ▷ C5×C23
UCSC1 ◁ C3×C72

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16905

Conjugacy classes & character table

8673 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33810, 76);