Finite Group Databasebeta

← Prev (#46798965) Next (#46798967) →

C3×C5×C72×D23 #46798966

order33810
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C72 · Schur multiplier (H2) = C7

Aliases

direct productC3×C5×C72×D23
unambiguous semidirect productC23⋊(C2×C3×C5×C72)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3×C5×C72D23
commutator, cosocle, hypocenterC23C2×C3×C5×C72
FrattiniC1G
Fitting, socleC3×C5×C72×C23C2
LCSG ▷ C23
UCSC1 ◁ C3×C5×C72

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16905

Conjugacy classes & character table

9555 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33810, 70);