Finite Group Databasebeta

← Prev (#38760758) Next (#38760760) →

AGL(1,𝔽5)×C23×C11⋊C5 #38760759

order25300
automorphism?
homologyAbelianization (H1) = C4×C5×C23 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽5)×C23×C11⋊C5
unambiguous semidirect product(C11×AGL(1,𝔽5))⋊(C5×C23)
unambiguous semidirect product(C11×AGL(1,𝔽5)×C23)⋊C5

Splittings

Fitting, socleC5×C11×C23 ⋊ C4×C5
derivedC5×C11 ⋊ C4×C5×C23
HallC5×C23×C11⋊C5 ⋊ C4
HallC5×C11⋊C5 ⋊ C4×C23
HallC11×C23 ⋊ C5×AGL(1,𝔽5)
SylowC11 ⋊ C5×AGL(1,𝔽5)×C23

Subgroups

subgroupG/H
center, hypercenterC23AGL(1,𝔽5)×C11⋊C5
commutator, hypocenterC5×C11C4×C5×C23
FrattiniC1G
Fitting, socleC5×C11×C23C4×C5
prime radicalD5×C23×C11⋊C5C2
cosocleD5×C11C2×C5×C23
LCSG ▷ C5×C11
UCSC1 ◁ C23

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1265

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25300, 96);