Finite Group Databasebeta

← Prev (#44538140) Next (#44538142) →

C11×C13×Dic55 #44538141

order31460
automorphism?
homologyAbelianization (H1) = C4×C11×C13 · Schur multiplier (H2) = C1

Aliases

direct productC11×C13×Dic55
unambiguous semidirect productC11⋊(C11×C13×Dic5)

Splittings

derivedC5×C11 ⋊ C4×C11×C13
HallC5×C112×C13 ⋊ C4
HallC112×C13 ⋊ Dic5
HallC5×C112 ⋊ C4×C13
SylowC112 ⋊ C13×Dic5
HallC5×C13 ⋊ C11×Dic11
SylowC5 ⋊ C11×C13×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C11×C13D55
commutator, hypocenterC5×C11C4×C11×C13
FrattiniC2C11×C13×D55
Fitting, socle, prime radicalC2×C5×C112×C13C2
cosocleC2×C5×C11C2×C11×C13
LCSG ▷ C5×C11
UCSC1 ◁ C2×C11×C13

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2860

Conjugacy classes & character table

8294 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31460, 81);