Finite Group Databasebeta

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C2×C25×D119 #26045384

order11900
isoclinismisoclinic class of D119
automorphism?
homologyAbelianization (H1) = C22×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C25×D119
unambiguous semidirect product(C2×C7)⋊(C25×D17)
unambiguous semidirect product(C2×C17)⋊(D7×C25)

Splittings

FittingC2×C7×C17×C25 ⋊ C2
derived, HallC7×C17 ⋊ C22×C25
HallC7×C17×C25 ⋊ C22
HallC17×C25 ⋊ C2×D7
HallC7×C25 ⋊ C2×D17
SylowC17 ⋊ C2×D7×C25
SylowC7 ⋊ C2×C25×D17

Subgroups

subgroupG/H
center, hypercenterC2×C25D119
commutator, hypocenterC7×C17C22×C25
FrattiniC5C2×C5×D119
FittingC2×C7×C17×C25C2
socleC2×C5×C7×C17C2×C5
prime radicalC2×C5×D119C5
cosocleC5×C7×C17C22×C5
LCSG ▷ C7×C17
UCSC1 ◁ C2×C25

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3050 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C25×C17⋊AGL(1,𝔽7), D3×C25×D119, C2×C25×D357, …
maximal normal subgroup ofC2×C25×C17⋊AGL(1,𝔽7), C2×C3×C25×D119
maximal quotient ofD3×C25×D119, C2×C25×D357, C2×C3×C25×D119

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11900, 33);