Finite Group Databasebeta

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C2×C23×D385 #47978490

order35420
automorphism?
homologyAbelianization (H1) = C22×C23 · Schur multiplier (H2) = C2

Aliases

direct productC2×C23×D385
unambiguous semidirect product(C2×C5)⋊(C23×D77)
unambiguous semidirect product(C2×C7)⋊(C23×D55)
unambiguous semidirect product(C2×C11)⋊(C23×D35)

Splittings

Fitting, socleC2×C5×C7×C11×C23 ⋊ C2
derived, HallC5×C7×C11 ⋊ C22×C23
HallC5×C7×C11×C23 ⋊ C22
HallC7×C11×C23 ⋊ C2×D5
HallC5×C11×C23 ⋊ C2×D7
HallC5×C7×C23 ⋊ C2×D11
HallC11×C23 ⋊ C2×D35
HallC7×C23 ⋊ C2×D55
HallC5×C23 ⋊ C2×D77
HallC7×C11 ⋊ C2×D5×C23
HallC5×C11 ⋊ C2×D7×C23
HallC5×C7 ⋊ C2×D11×C23
SylowC11 ⋊ C2×C23×D35
SylowC7 ⋊ C2×C23×D55
SylowC5 ⋊ C2×C23×D77

Subgroups

subgroupG/H
center, hypercenterC2×C23D385
commutator, cosocle, hypocenterC5×C7×C11C22×C23
FrattiniC1G
Fitting, socleC2×C5×C7×C11×C23C2
LCSG ▷ C5×C7×C11
UCSC1 ◁ C2×C23

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17710

Conjugacy classes & character table

8924 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 124);