Finite Group Databasebeta

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C3×C7×D805 #46798974

order33810
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×D805
unambiguous semidirect productC5⋊(C3×C7×D161)
unambiguous semidirect productC23⋊(C3×C7×D35)

Splittings

Fitting, socle, HallC3×C5×C72×C23 ⋊ C2
derivedC5×C7×C23 ⋊ C2×C3×C7
HallC5×C72×C23 ⋊ C2×C3
HallC3×C72×C23 ⋊ D5
HallC72×C23 ⋊ C3×D5
HallC3×C5×C72 ⋊ D23
HallC3×C5×C23 ⋊ C7×D7
HallC5×C72 ⋊ C3×D23
HallC3×C72 ⋊ D115
HallC5×C23 ⋊ C3×C7×D7
HallC3×C23 ⋊ C7×D35
SylowC72 ⋊ C3×D115
SylowC23 ⋊ C3×C7×D35
HallC3×C5 ⋊ C7×D161
SylowC5 ⋊ C3×C7×D161

Subgroups

subgroupG/H
center, hypercenterC3×C7D805
commutator, cosocle, hypocenterC5×C7×C23C2×C3×C7
FrattiniC1G
Fitting, socleC3×C5×C72×C23C2
LCSG ▷ C5×C7×C23
UCSC1 ◁ C3×C7

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4830

Conjugacy classes & character table

8484 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33810, 78);