Finite Group Databasebeta

← Prev (#23780392) Next (#23780394) →

C32×C5×D5×C23 #23780393

order10350
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C23 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×D5×C23
unambiguous semidirect productC5⋊(C2×C32×C5×C23)

Splittings

Fitting, socle, HallC32×C52×C23 ⋊ C2
derivedC5 ⋊ C2×C32×C5×C23
HallC52×C23 ⋊ C2×C32
HallC32×C52 ⋊ C2×C23
SylowC52 ⋊ C2×C32×C23

Subgroups

subgroupG/H
center, hypercenterC32×C5×C23D5
commutator, cosocle, hypocenterC5C2×C32×C5×C23
FrattiniC1G
Fitting, socleC32×C52×C23C2
LCSG ▷ C5
UCSC1 ◁ C32×C5×C23

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4140 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×C5×D5×D23, C32×C5×AGL(1,𝔽5)×C23, C32×C5×C23⋊AGL(1,𝔽5), …
maximal normal subgroup ofC32×C5×D5×D23, C32×C5×AGL(1,𝔽5)×C23, C32×C5×C23⋊AGL(1,𝔽5), …
maximal quotient ofC32×C5×Dic5×C23, C2×C32×C5×D5×C23

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10350, 67);