Finite Group Databasebeta

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C2×C5×D23×C11⋊C5 #38760770

order25300
automorphism?
homologyAbelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C5×D23×C11⋊C5
unambiguous semidirect productC23⋊(C22×C5×C11⋊C5)
unambiguous semidirect product(C2×C23)⋊(C2×C5×C11⋊C5)
unambiguous semidirect product(C2×C11×D23)⋊C52
unambiguous semidirect product(C2×C5×C11×D23)⋊C5

Splittings

Fitting, socleC2×C5×C11×C23 ⋊ C2×C5
derived, HallC11×C23 ⋊ C22×C52
HallC5×C23×C11⋊C5 ⋊ C22
HallC2×C11×D23 ⋊ C52
SylowC23 ⋊ C22×C5×C11⋊C5
SylowC11 ⋊ C2×C52×D23

Subgroups

subgroupG/H
center, hypercenterC2×C5D23×C11⋊C5
commutator, cosocle, hypocenterC11×C23C22×C52
FrattiniC1G
Fitting, socleC2×C5×C11×C23C2×C5
LCSG ▷ C11×C23
UCSC1 ◁ C2×C5

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2530

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25300, 107);