Finite Group Databasebeta

#1395×D67 #30770820

order17152
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct product#1395×D67

Splittings

FittingC67×#1395 ⋊ C2
SylowC67 ⋊ C2×#1395

Subgroups

subgroupG/H
centerC4#99×D67
commutatorC2×C4×C67C2×C42
FrattiniC2×#41C22×D67
FittingC67×#1395C2
socleC2×C67C2×#342
prime radicalC2×#41×D67C22
cosocleC2×#41×C67C23
hypercenter#1395D67
hypocenterC67C2×#1395
LCSG ▷ C2×C4×C67 ▷ C22×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #1395

766 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 84557);