Finite Group Databasebeta

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C2×C5⋊D595 #26045459

order11900
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C5⋊D595
unambiguous semidirect product(C2×C5)⋊D595
unambiguous semidirect product(C2×C7)⋊(C5⋊D85)
unambiguous semidirect product(C2×C17)⋊(C5⋊D35)

Splittings

Fitting, socleC2×C52×C7×C17 ⋊ C2
derived, HallC52×C7×C17 ⋊ C22
HallC52×C17 ⋊ C2×D7
HallC52×C7 ⋊ C2×D17
HallC7×C17 ⋊ C2×C5⋊D5
SylowC52 ⋊ C2×D119
SylowC17 ⋊ C2×C5⋊D35
SylowC7 ⋊ C2×C5⋊D85

Subgroups

subgroupG/H
center, hypercenterC2C5⋊D595
commutator, cosocle, hypocenterC52×C7×C17C22
FrattiniC1G
Fitting, socleC2×C52×C7×C17C2
LCSG ▷ C52×C7×C17
UCSC1 ◁ C2

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2978 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C17⋊#11760386, C2×C17⋊#11760384, C2×C5⋊(C5⋊(C17⋊AGL(1,𝔽7))), …
maximal normal subgroup ofC2×C17⋊#11760386, C2×C17⋊#11760384, C2×C5⋊(C5⋊(C17⋊AGL(1,𝔽7))), …
maximal quotient ofD3×C5⋊D595, C2×C3×C5⋊D595, C2×C3⋊(C5⋊D595)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11900, 108);