Finite Group Databasebeta

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C5×C72×D69 #46798978

order33810
automorphism?
homologyAbelianization (H1) = C2×C5×C72 · Schur multiplier (H2) = C7

Aliases

direct productC5×C72×D69
unambiguous semidirect productC3⋊(C5×C72×D23)
unambiguous semidirect productC23⋊(C5×D3×C72)

Splittings

Fitting, socle, HallC3×C5×C72×C23 ⋊ C2
derived, HallC3×C23 ⋊ C2×C5×C72
HallC5×C72×C23 ⋊ D3
HallC3×C72×C23 ⋊ C2×C5
HallC72×C23 ⋊ C5×D3
HallC3×C5×C72 ⋊ D23
HallC3×C5×C23 ⋊ C2×C72
HallC3×C72 ⋊ C5×D23
HallC5×C23 ⋊ D3×C72
SylowC23 ⋊ C5×D3×C72
HallC3×C5 ⋊ C72×D23
SylowC3 ⋊ C5×C72×D23

Subgroups

subgroupG/H
center, hypercenterC5×C72D69
commutator, cosocle, hypocenterC3×C23C2×C5×C72
FrattiniC1G
Fitting, socleC3×C5×C72×C23C2
LCSG ▷ C3×C23
UCSC1 ◁ C5×C72

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16905

Conjugacy classes & character table

8820 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33810, 82);