Finite Group Databasebeta

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C32×C5×Dic65 #26043524

order11700
isoclinismisoclinic class of D65
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×Dic65

Splittings

derivedC5×C13 ⋊ C32×C4×C5
HallC32×C52×C13 ⋊ C4
HallC52×C13 ⋊ C32×C4
HallC32×C52 ⋊ Dic13
HallC32×C13 ⋊ C5×Dic5
SylowC52 ⋊ C32×Dic13
SylowC13 ⋊ C32×C5×Dic5

Subgroups

subgroupG/H
center, hypercenterC2×C32×C5D65
commutator, hypocenterC5×C13C32×C4×C5
FrattiniC2C32×C5×D65
Fitting, socle, prime radicalC2×C32×C52×C13C2
cosocleC2×C5×C13C2×C32×C5
LCSG ▷ C5×C13
UCSC1 ◁ C2×C32×C5

192 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3060 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11700, 371);