Finite Group Databasebeta

← Prev (#44477472) Next (#44477474) →

C32×C5×Dic169 #44477473

order30420
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×Dic169

Splittings

derived, SylowC169 ⋊ C32×C4×C5
HallC32×C5×C169 ⋊ C4
HallC32×C169 ⋊ C4×C5
HallC5×C169 ⋊ C32×C4

Subgroups

subgroupG/H
center, hypercenterC2×C32×C5D169
commutator, hypocenterC169C32×C4×C5
FrattiniC2×C13C32×C5×D13
FittingC2×C32×C5×C169C2
socle, prime radicalC2×C32×C5×C13D13
cosocleC2×C169C2×C32×C5
LCSG ▷ C169
UCSC1 ◁ C2×C32×C5

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30420

Conjugacy classes & character table

7740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 62);