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C41×(C49⋊C3)⋊C4 #37562996

order24108
automorphism?
homologyAbelianization (H1) = C3×C4×C41 · Schur multiplier (H2) = C1

Aliases

direct productC41×(C49⋊C3)⋊C4
unambiguous semidirect product(C49⋊C3)⋊(C4×C41)
unambiguous semidirect productDic49⋊(C3×C41)
unambiguous semidirect product(C41×Dic49)⋊C3

Splittings

derived, SylowC49 ⋊ C3×C4×C41
HallC41×Dic49 ⋊ C3
HallC41×C49⋊C3 ⋊ C4
HallC41×C49 ⋊ C3×C4
HallDic49 ⋊ C3×C41
HallC49⋊C3 ⋊ C4×C41

Subgroups

subgroupG/H
center, hypercenterC2×C41D49⋊C3
commutator, hypocenterC49C3×C4×C41
FrattiniC2×C7C41×AGL(1,𝔽7)
FittingC2×C41×C49C2×C3
socleC2×C7×C41AGL(1,𝔽7)
prime radicalC2×C41×C49⋊C3C2
cosocleC2×C49C2×C3×C41
LCSG ▷ C49
UCSC1 ◁ C2×C41

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8036

Conjugacy classes & character table

1148 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24108, 3);