Finite Group Databasebeta

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C32×C11⋊#63118 #38788176

order25740
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC32×C11⋊#63118
unambiguous semidirect productC11⋊(C32×#63118)

Splittings

Fitting, socle, HallC32×C5×C11×C13 ⋊ C4
derived, HallC5×C11×C13 ⋊ C32×C4
HallC32×C11×C13 ⋊ Dic5
HallC32×C5×C13 ⋊ Dic11
HallC32×C5×C11 ⋊ #261
HallC11×C13 ⋊ C32×Dic5
HallC32×C13 ⋊ Dic55
HallC32×C11 ⋊ #63118
HallC5×C13 ⋊ C32×Dic11
HallC5×C11 ⋊ C32×#261
HallC32×C5 ⋊ C11⋊#261
SylowC13 ⋊ C32×Dic55
SylowC11 ⋊ C32×#63118
SylowC5 ⋊ C32×C11⋊#261

Subgroups

subgroupG/H
center, hypercenterC32C11⋊#63118
commutator, hypocenterC5×C11×C13C32×C4
FrattiniC1G
Fitting, socleC32×C5×C11×C13C4
prime radicalC32×C5×C11×D13C2
cosocleC5×C11×D13C2×C32
LCSG ▷ C5×C11×C13
UCSC1 ◁ C32

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6435

Conjugacy classes & character table

2007 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 407);