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C2×C5×C5⋊AGL(1,𝔽23) #38760752

order25300
automorphism?
homologyAbelianization (H1) = C22×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C5⋊AGL(1,𝔽23)
unambiguous semidirect product(C2×C5)⋊(C5×AGL(1,𝔽23))
unambiguous semidirect product(C2×D115)⋊(C5×C11)
unambiguous semidirect product(C2×C23⋊C11)⋊(C5×D5)
unambiguous semidirect product(C2×C5×D115)⋊C11

Splittings

Fitting, socleC2×C52×C23 ⋊ C2×C11
derivedC5×C23 ⋊ C22×C5×C11
HallC52×C23⋊C11 ⋊ C22
HallC2×C5×D115 ⋊ C11
HallC52×C23 ⋊ C22×C11
HallC23⋊C11 ⋊ C2×C5×D5
SylowC52 ⋊ C2×AGL(1,𝔽23)
SylowC23 ⋊ C2×C5×D5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5C5⋊AGL(1,𝔽23)
commutator, cosocle, hypocenterC5×C23C22×C5×C11
FrattiniC1G
Fitting, socleC2×C52×C23C2×C11
LCSG ▷ C5×C23
UCSC1 ◁ C2×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 460

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25300, 89);