Finite Group Databasebeta

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C17×C25×Dic19 #44568013

order32300
automorphism?
homologyAbelianization (H1) = C4×C17×C25 · Schur multiplier (H2) = C1

Aliases

direct productC17×C25×Dic19
unambiguous semidirect productC19⋊(C4×C17×C25)

Splittings

derived, SylowC19 ⋊ C4×C17×C25
HallC17×C19×C25 ⋊ C4
HallC19×C25 ⋊ C4×C17
HallC17×C19 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC2×C17×C25D19
commutator, hypocenterC19C4×C17×C25
FrattiniC2×C5C5×C17×D19
FittingC2×C17×C19×C25C2
socle, prime radicalC2×C5×C17×C19C2×C5
cosocleC2×C5×C19C2×C5×C17
LCSG ▷ C19
UCSC1 ◁ C2×C17×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32300

Conjugacy classes & character table

9350 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32300, 2);