Finite Group Databasebeta

← Prev (#44542070) Next (#44542072) →

C5×C11×AGL(1,𝔽5)×C29 #44542071

order31900
automorphism?
homologyAbelianization (H1) = C4×C5×C11×C29 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×AGL(1,𝔽5)×C29

Splittings

Fitting, socle, HallC52×C11×C29 ⋊ C4
derivedC5 ⋊ C4×C5×C11×C29
HallC52×C29 ⋊ C4×C11
HallC52×C11 ⋊ C4×C29
SylowC52 ⋊ C4×C11×C29

Subgroups

subgroupG/H
center, hypercenterC5×C11×C29AGL(1,𝔽5)
commutator, hypocenterC5C4×C5×C11×C29
FrattiniC1G
Fitting, socleC52×C11×C29C4
prime radicalC5×D5×C11×C29C2
cosocleD5C2×C5×C11×C29
LCSG ▷ C5
UCSC1 ◁ C5×C11×C29

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6380

Conjugacy classes & character table

7975 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31900, 106);