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C5×C5⋊#11716322 #34093033

order19950
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C5⋊#11716322
unambiguous semidirect productC5⋊(C5×#11716322)

Splittings

Fitting, socle, HallC52×C7×C19 ⋊ C2×C3
derivedC5×C7×C19 ⋊ C2×C3×C5
HallC52×#87705 ⋊ C2
HallC5×C7×D95 ⋊ C3
HallC5×D95 ⋊ ΓL(1,𝔽8)
HallC52×C19 ⋊ C2×ΓL(1,𝔽8)
Hall#87705 ⋊ C5×D5
HallC52×C7 ⋊ D19⋊C3
HallC7×C19 ⋊ C3×C5×D5
SylowC52 ⋊ #11716322
SylowC19 ⋊ C5×D5×ΓL(1,𝔽8)
SylowC7 ⋊ C5×C5⋊(D19⋊C3)

Subgroups

subgroupG/H
center, hypercenterC5C5⋊#11716322
commutator, cosocle, hypocenterC5×C7×C19C2×C3×C5
FrattiniC1G
Fitting, socleC52×C7×C19C2×C3
LCSG ▷ C5×C7×C19
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1330

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19950, 72);